We plug in the bricks at the same location that the router and telco equipment is at. At the power brick, 1 CAT-5 line goes to the router, the other line goes to the WAP. We use these in my church buildings.
That's using power injectors and the WAP is fed power over the Ethernet link. That's fine, if you only have one or two devices. I meant using power bricks at the same location as the WAP and plugging it in directly. Firstly, it's not always possible as there isn't a power socket nearby, and secondly as I said, some idiot might switch it off.
I use a switch with PoE built in, that way I don't need a power injector for each device. At home, I only have a couple of IP phones, but when I was at work we had loads of devices all over the place so a separate power brick for each one would have been unmanageable.
By the way, Cat 5 is a bit out of date now, you might want to think about using Cat 6, or at the very least 5e.