@SZDBLLC,
If you are sure that your home is using regular Cat5 and not 5E, then definitely yes. CAT5 was only used for a short period and is relatively uncommon to find nowadays, but can still be found in home installations from the period.
CAT5 Cables are designed to give between 10 and 100 Mbps, well below what your network is capable of. Saying that, this is often enough for client connections, but not enough to support a high speed network. You may try using a switch to distribute the network to some of your devices, such as a TV with the CAT5 wiring, while using the wireless backhaul for other connections. Doing this would free up some of the bandwidth on the wireless backhaul and may provide a better overall experience.
Depending on your setup, you may look into running a newer cable to your main living area, so that this node would be given a full speed connection to communicate back to the main node. From there, the other decos may take advantage of this and daisy chain together.