Well that's because that was a 'phone tech' that says he can install cat5 because that's what builders asked back then. That is how phone was installed back in the day as home runs were expensive and so were punchdown blocks. Home run network wiring back then wasn't even understood as a concept in residential construction.
You can use a cable toning tool (mine was about $100) to figure out where everything ends up, and now that I think about it, a toning tool would be quite useful as one of the jacks on one of the outlets will end up going to the phone company, which you don't want connected to your ethernet network and vice-versa. So I would get a toning tool like either of these (the fluke one is the one I think I have):
The Noyafa NF-811 is a cost friendly wire tracker consisting of a transmitter and a receiver. It can be used to trace network cables, telephone cables, and it identifies cable's continuity quality. It's an ideal network tool for techs who work frequently with communication and integrated wiring.
www.techtoolsupply.com
You will need the alligator clips as you will not be plugging in a cable every time. The first thing you would need to do is go to every phone jack and open it up and separate the wires if they have been 'daisy chained' together. Ie, if two different sets of wires have been connected to the same jack or each other. Once you have done that then you can start by connecting alligator clips from the tone generator to one of the cables from the jack by your router. This will send a tone down that wire. Using the detector, you will go to each room and listen for tones on each wire. It will only sound on one of them. Once you find this you can punch down a jack on both the wire you found as well as the one by your router. If you do this right, you should be able to now connect the new jack by the router and then connect a laptop or switch to the new jack in the room and get ethernet. This is essentially the core of the process to re-wire all the jacks in your house.
I wouldn't worry about the limits of cat5. My parents house was built in 1995 before cat5e was even a standard and wireless didn't exist yet. We had wire ran for 2 ethernet jacks in each room with the best 400Mhz wire we could find. Today, almost 25 years later, almost all the jacks can run gigabit without a problem. Some of the terminations were not done right as was par for the course back in that day since no one in residential construction understood what networking wiring was, so those jacks only pass 100Mbps, but I know if I re-terminate them they should work on gigabit. And the good thing is that if they work on gigabit, they are also going to be good for 2.5Gb. Now that I understand the timeframe of the construction, it makes perfect sense to see the phone wiring daisy chaining.