In a home network, does it matter if I have Cat5, 6, 7?
As you probably understand, it depends on what you typically do with your home network.
That said, if you're referring to Cat 5 and not Cat 5e, I'd say that it could matter. But I doubt that it would matter if you're comparing Cat 5e and Cat 6.
For most home use, I think the difference between Cat 5e and Cat 5 is more important (for now) than the difference between Cat 6 and Cat 5e. Particular Cat 5 cables can be capable of the same kinds of speeds as Cat 5e over shorter distances, but their specs are such that they won't necessarily be. And at this point we move enough data that the difference could matter.
If someone is running new cables (or buying new cables to connect devices to each other or to wall jacks), I'd recommend that they get Cat 6. In the future it might matter to have that instead of Cat 5e. But if someone already has Cat 5e installed, and they aren't experiencing problems that they think are caused by it, then for most people I wouldn't recommend that they go to the trouble or expense to change.
Keep in mind that the way we typically measure file sizes is different from the way we typically measure speeds. The former is usually in mega
bytes, the latter is often in mega
bits (per second). A theoretical speed of 100 Mbps (which the Cat 5 spec provides) means moving 12.5 MBs per second - maybe a couple of mp3s each second or five minutes for an HD movie.