Unless the cable is causing errors, Cat 6 won’t have faster data transfer than Cat 5 or Cat 5e.
That said, off-the-shelf Cat 5 cables vary greatly in quality, so you are more likely not to have errors using a Cat 6 cable for Gigabit.
For example, as I go through my cable bin, I have Cat 5 cables that link up at Gigabit no problem. I also have Cat 5 cables that don’t link at Gigabit. Really depends on the cable.
My Cat 5e cables (though I have far fewer of these) have no problem at Gigabit.
My Cat 6 cables have no problem at Gigabit.
It’s kind of like CPUs - you can buy a cheaper CPU and maybe overclock it to the more expensive CPU’s speed, but if you want to guarantee you’ll get the full speed, you should buy the more expensive CPU to begin with.
BTW: Cat 6 cables are cheaper at Fry’s (or online sites like Monoprice than they are at Best Buy… not that I dislike Best Buy, I’m a Premier Silver RZ member, after all.