In the ruy lopez position above, why black should not play b5?

He would get captured by the black pawn

ok, but what after this?

Castle apparently, with the idea of opening the a file for the rook if you take the bishop.

Not sure if that is good enough compensation for the doubled pawn and bishop pair though, but white seems to have success.

This move loses a pawn and gains a open file for White. 

White will capture the e5 pawn if Black moves ...Na5

Playing ...b5 quickly will weakens the dark-squares for Black. And will give White an powerful d5 post for Bishop.

What about Qg5 after your diagram, forking knight and g2 pawn?

6...Qg5 7.Bxf7+ Ke7 8.d4 Qxg2 9.Rf1 Qxh2 10.Bg5+ is better for White, with an exposed King.

or 6...Qg5 7.Qf3! (7...Qxe5 8.Qxf7+ Kd8 9.Qxf8+ Qe8 10.Qxe8 Kxe8 is better for White) 7...Nxb3 8.Qxf7+ Kd8 9.Qxf8#

Thanks, I'll take a look through later.

The point of ...a6, ...b5, ...Na5 doesn't helps Black to develop.