A 5 channel amp would allow him to power 5 speakers. It sounds like he has 10 speakers, so he'd need a pair of 5 channel amps.
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In addition to needing two five channel amps, in order to get "equal" sound, all five channels have to have the same power output. For example, some cheap HT receivers don't have as much power for the rear surrounds.
If this is just a convenience thing to get sound to all the rooms for mostly background listening, a switching box is probably a lot more economical.
Niles makes multi channel amps that are really nice. I really like the 12 channel sherbourne. This could eliminate the multi speaker selector. My guess is that the selector is actually hurting the sound quality anyway. Older Adcom units tended to have "melt downs".
I'm using a really nice 2 channel amp with a top of the line niles selector and am very happy.