the one filter before it, then run Cat5 to both the computers up the side
of the house. Anything wrong with this plan?

Similar to what I did, except I ran the cables down the house.

You may find that the CAT5 cable is not UV stable and will break down after
a few years...

I ran my cable down the back of the gutter downpipe (fastened with cable
ties) so that it wouldn't be visible. I also painted over the cable with the
same paint as the downpipe to help preserve it longer(?) So far so good...

Colin