Can a 6x6 post be used horizontally to support the walls of a shed?
Almost absolutely. A 5' span is small enough that there's almost no shed you could build that wouldn't be fine on those timbers. It's only if you're talking 20' walls and a huge roof span that I'd be concerned.
If you want a more confident answer, tell us more about your shed. Size, wall sheathing, floor framing, and other factors are relevant.
Note that they should really be pressure-treated or isolated from the concrete and protected from ground moisture (splash).