I do agree, if they are already running Category 5e and not Category 5 cable, there isn't enough difference in the two to make that much of a difference.
I do disagree...
partially...
with the assertion that you must use Cat 7 cable for 10Gbase, we use Cat6 at work and it works fine. I would NOT use Cat6 in a high interference area such as when the Structured Wiring Panel is right next to say a high power audio amplifier, or your main breaker panel is right next to it. However for short runs (under 100') in a data center, it has worked flawlessly. HOWEVER it is also true that frequently folks do run into problems using Cat6 on 10Gbase networks. Again in electrically noisy environments in particular Cat6 is a BAD idea for 10G...
Now with all of that hot air expended. Like I said, if you already have sufficient Cat5e going to where you want it to go, and they want to upcharge you $1K to run Cat6. Save your money. The difference in cost between a 1000' box of quality cat5e, and cat5e connectors versus cat 6 is maybe $100.00. Toss into the mix that chances are they will be tying into a cat5e rated patch panel for your structured wiring panel (not many of them are Cat6 for some reason), and it makes sense to stay with 5e.
The cable will already be there, so if you want to upgrade later, it is a pretty simple process to back pull say Cat7 if you ever want to go that fast and can afford the connectors, cable, NICs, switches etc... Or if prices drop radically... (10G over any media, copper, filber, whatever is EXPENSIVE!).
Best of luck with the build, and enjoy the new house!