5e will not just handle gigabit, it's enough to run 2.5gig at spec to 100 meters.

5 has the same bandwidth as 5e but allows more crosstalk. And gigabit is intended to work on cat5. If gigabit is not working on cat5 cables <50m, I put my money on there being something wrong with the hardware/install in that house.

The spec for older ethernet standards is with 100 meters of cabling with most of it un dense conduit. You can get away with lesser cable when runs are shorter and not in dense conduit. I had a run of mixed cat5e and cat3 that did gigE just fine. I'm not sure I've ever seen actual cat5 in the wild, but from what I've heard, most cat5 will test to cat5e spec too.

I have 10g-base-t running reliably on cat5e as well. (30ish meters)

GigE works totally fine on bog standard 25 year old Cat5 over 100s of ft.