posetcay: As it stands, S5 doesn't actually gain a liberty. This makes the tsumego trivial to solve without ever exchanging S5. Therefore I modified the problem a bit to make S5 a crucial part of solution by removing S8 stone and adding 1 more liberty to the P3 group.
In principle they could, but S12 S11 is a bad exchange; gives opponent ponnuki for free.