@network_user 

You start with the solution(s) and then provide problem description. It usually works better the opposite way.

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My understanding is, this is what you have and correct me if I am wrong:

1. Internet speed at 50Mbps/10Mbps. 

2. ADSL modem/router, with WiFi 2.4GHz and 5GHz. Must be router (not just modem) if it provides WiFi. It would be useful if you could share ADSL modem/router brand name/model number.

3. If you stay with ADSL, 50Mbps is as fast as you could get. If your provider plans offering coax/fibre, the Internet speed may increase dramatically. Do you know if they have such plans?

4. You have wired home network consisting of 10 Gigabit switch, PCs and NAS. This home network not connected to modem/router and has no access to the Internet. Question: how did you set that network, do your computers and NAS use static IP addresses or do you run DHCP/DNS server on NAS?

You want to connect your home network to ADSL modem/router, using one of switch ports. The distance between them is about 25 feet and you can't run Ethernet cable between home network and modem (if you could, you wouldn't be posting your question here).

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Trying to link ADSL modem with home network by WiFi is an option, but there are other options worth to investigate, before discussing wireless link.

Hence my questions:

1. Can you run Ethernet cable between modem and switch on a temporary basis? If you can, that may help with reconfiguration of your home network. When you link your PCs and NAS to ADSL modem/router, it would make sense to use its DHCP and DNS.

2. Do you maybe have coax TV cable that starts around ADSL modem and terminates around the switch? 

3. Is it possible you have two electric outlets on same circuit breaker, one near ADSL modem and one near the switch?

4. Do you have smartphone you can install network analyzer on and use to test signal strength? That may help to guesstimate how good wireless link between ADSL modem and networking switch can be, if wired link is out of the question.

  @Alexandre. 

Thanks for your reply.

1. Yes. Up to 50Mbps (download) and up to 10Mbps (upload)

2. It is a Sagemcom Fast 5566. Tried to provide a link but the forum system does not accept it.

I asked my ISP the type of device. At first he said modem+router+switch but later on he said technically, it is an ADSL modem. 

3. About two months ago, the ISP sent a contractor to "upgrade" the building internet to fiber. I asked them what services would be available and the guy said that he had no idea as he came here to do some wiring job. He told me to ask my ISP. I contacted my ISP four times as recent as this week and they still said that the modem and service plan are the best they could offer now and they have no idea when a faster service would be available. They did not even know their contractor came to the condo to do some wiring. One of them did mention that in case fiber is available and I opt for the upgrade, I would lose the phone lane line and I would have to use VoIP which would not work in case of internet connection trouble. After hearing that, a family member already complained. So I won't count on the upgrade. 

4. This is a very good question. I just ordered a 10G switch today. I have not setup the NAS as I need something to bridge between the two rooms. So far, everything is connected to the internet though WiFi connection. Internet connection is very good and the speed in practice is very fast. It is like I were using the ethernet in university. The main reason I am looking for a method to connect the two rooms is that somebody mentioned that although I should connect the NAS and computers to a switch for the fastest 10GbE connections, I still need to use another 1GbE port from the NAS to connect to a router so that I could update its software and firmware. For the NAS, I don't plan to access it from outside home network. I will not open it to the internet due to security reason. 

  @network_user 

Sagemcom Fast 5566 is a router. It has four gigabit Ethernet ports you can use to connect wired devices to it.

Your selection of hardware to connect the two rooms is not the optimal one.

I am going to list the options you might have, and when you pick the one which is feasible and let me know, I'll go through more details for it and what hardware you should be getting:

1. If you have TV coaxial cable that starts in one room and terminates in second room, a pair of MoCA adapters can create wired Ethernet link between them.

2. If you have two electrical outlets on same circuit breaker, one in one room and another in second room, a pair of powerline adapters can create wired Ethernet link between them.

3. A poor man's solution would be once in a while to just grab NAS, carry it to where Sagemcom Fast 5566 is, wire to the router and check for software updates. Then, carry NAS back. It depends of course on how heavy NAS is. Mine is two bay Synology DS220+, reasonably easy to move around.

4. If none of the above, I can suggest you the WiFi range extender which should do the work for you. 

  @Alexandre. 

Thank you for the suggestions.

1. That Sagemcom device is connected to another device which connects to my TV. I tried MoCA adapters already but failed. Just returned the product. Looks like the coax ports in the two areas are not connected.

2. I also considered that but some mentioned that powerline adapters have stability issue when powerful electrical appliances are use. Given that stability is very important for NAS, I decided to forget about that choice. 

3. Mine is a DS1522+. I considered that option. I have never used NAS, switch nor Mesh system before. If I just connect my NAS and the computers to a switch, do I still need to connect the switch to the router in order to assign the IP address for each device automatically? If I opt for that poor man's solution, once I have disconnected the NAS and reconnect it later, will the NAS get a new IP address or still get to keep the one it gets when I connect it to the switch for the first time? Will it mess up something if I manually disconnect and reconnect the NAS for software upgrade? I would prefer not to manually assign IP address as I might mess up something. I don't know much about networking.

4. I planned to buy a RE815XE but somebody recommended to use a Deco mesh system rather than range extender because range extender could lose throughput as different devices compete for the traffic. Knowing the old router and the service plan, I considered to buy the RE650 and upgrade later when my internet provide can offer a faster system and service plan.

  @network_user 

Still, consider powerline adapters, especially if you could get them from the place with good return policy. While it is true that they are sensitive to appliances plugged to outlets, WiFi link is also sensitive to wireless interference. A microwave or cordless phone could impact WiFi link, as well as WiFi networks from neighbors. You wouldn't know which is better for your place, until you try.

For the Internet speed you have, it does not make sense to go with the WiFi mesh. A simple range extender can do the job.

RE815XE is an overkill, considering your Sagecom router specs and Internet speed. Just go with inexpensive WiFi range extender that has the following:

1. Supports 2.4GHz and 5GHz;

2. Does not support WiFi 6, WiFi 6E or WiFi7 - these are not necessary, make device more expensive and you'll be paying for something you won't be using;

3. Must have Ethernet port (obviously);

4. Should have signal quality indicator, to help troubleshoot connectivity issues.

TP-Link RE650 is a good choice. You can also go with RE550 or RE450. 

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Before you buy WiFi range extender, do the simple test. Bring smartphone or tablet connected to Sagecom WiFi to where your NAS will be and where range extender will be. From that place, run speed test on smartphone/tablet. If you are getting close to 50Mbps download speeds in speed test, that means WiFi range extender will do the job. If multiple speed tests show much worse speeds, that could mean WiFi link may not be good and you may need to research other options - or find different place for range extender. Use smartphone/tablet to find optimal place, before you buy.

  @Alexandre. 

Thanks. I will get a RE650 on tomorrow and try out this option.

Which iOS app do you recommend to do the speed test?

About the computer room... Internally, the NAS and computers are connected to each other via a 10GbE switch. Am I correct that for backup and file transfer among these devices, they are not limited by the slow router and internet plan?

I plan to have my main PC connected to the switch and then to the NAS via 10GbE ports. For internet access, it just uses Wifi as I don't experience any slowness. If I connect my main PC, a laptop or a tablet to the extended Wifi (be it RE650 or a mesh system), rather than the Wifi provided by the router, am I correct that the transfer speed between the device and the NAS will increase but for tasks that involves the internet, the speed will still be limited by the router and the service plan? One application for such potential increase in speed using a faster secondary network in the computer room is backup the entire iPad or transfer its photos and videos to the NAS.

  @network_user 

We are drifting away from the original topic and to the limits of my networking knowledge.

I expect switch to route traffic between two devices connected to it without passing it to default gateway. In any case, it'll work the same does not matter with what means you are going to link your wired network to ISP router. So, just build what you want to and test it. Your WiFi link to Sagecom will be gigabit at most, and most likely even less. You wired devices are on 10 gigabit, you said. Just copying large file from NAS to PC will tell you how the data flows.

If I am wrong and all traffic goes through the default gateway, you'll have to research the following topics for your PCs and NAS: setting static routes, multiple default gateways and/or making NAS default gateway.

As for the speed test, you can open fast.com web site in smartphone browser to run speed test or install Ookla Speedtest app from app store.

  @Alexandre. 

Using fast.com with existing router from ISP:

iPad

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Internet Speed: 59 Mbps

Upload: 8.8 Mbps

Latency: 15 ms (unloaded), 33 ms (loaded)

iPhone

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Internet Speed: 59 Mbps

Upload: 9.9 Mbps

Latency: 14 ms (unloaded), 35 ms (loaded)

PC

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Internet Speed: 60 Mbps

Upload: 8.9 Mbps

Latency: 13 ms (unloaded) 32 ms (loaded)

  @network_user 

Excellent result: you are getting speeds of your Internet link. WiFi range extender can do the same, so it should work for you. No need for WiFi mesh.