The answer comes in a couple of different parts.
1) Quite strictly speaking, the IP phones can share the same infrastructure, cabling, and bandwidth as your LAN.
2) Usually, the IP phones are installed with separate infrastructure (routers, switches, etc.) and cabling. This is far more common, and usually to be recommended.
The reasons for the separate infrastructure largely have to do with bandwidth – most networks run a little shy of bandwidth at certain times of the day anyway, even before you think about adding real-time voice traffic, which is quite sensitive to delayed packets.
Cisco makes a nice line of wireless IP phones that I have experience with; I’m sure other vendors can provide them, too — the problem is that the bandwidth is even more constrained with 802.11b/g than it is with the network cable.
Last comment: don’t use CAT5. Use at least CAT5e. And if you’re putting in new cable, there is no good reason not to pay a few cents per foot extra and install CAT6. The labor charge is the same, and the bandwidth possibilities are greatly enhanced with CAT6.