Take your measurement by connecting your computer directly to the modem, not a router. It may then read the advertised speed.
Not necessarily true but I am not going to argue it. I have tested here with computer on cat5 vs wireless, downloading a file on all 6 computers at the same time, and my speeds were within 2% on both, so that whole thing about a home router being a bottleneck isn't, and has never been, true. ...
I'm glad you aren't going to argue, because that would be an incorrect approach. Also, in your description, did you mean to say you have Cat5 cable, and not Cat5e or Cat6? Cat 5 has a maximum rated speed of 100Mbps (5e is 1000Mbps). This alone would throw off any results you would get. Testing WiFi speeds is even more problematic.
Cat 5 is no longer used in new installations. If you (or anyone else reading this) are paying for rated speed over 100Mbps, you should switch out all your Ethernet cables for Cat 5e. Of course, you must also have a modem that supports the higher speeds. When I changed from 100 to 400, I had to buy a new modem (or rent the ISP's).
PS to PianoBilly, the OP, I live two hours north of NYC, and my ISP's trunk line is based much closer, in Westchester County. No problems on Tuesday.