It is very unlikely that your home is wired with Cat 5. It is likely wired with 4 conductor POTS cable. My house was built in 86 and is wired with 4 conductor POTS cable. It is also probably stapled to the studs, so you can't just tie a Cat 5 cable onto the end of the cable and pull it through the other end.

If you have easy attic and/or crawlspace access, I would run new Ethernet cable with keystone plates in each room, maybe one on each side of the room - all run to a central closet (maybe a broom closet or your mechanical closet if you have one).

A long term project for me is to replace all the phone wiring in my home with Cat 6 cabling. My issue is my home is a two story so I do not have an easy way to run cables between floors without drywall work. Currently I'm making due with 802.11AC wireless - which is good enough certainly, but not as good as Ethernet.

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