I am somewhat surprised that nobody mentioned (or at least I didn't notice anyone mention) bidding 3S instead of 3C.
IMO that would have been a good bid (though I wouldn't quite go as far as to consider 3C a bad bid).
Given the way that the auction has actually developed, I think this is a close call between 5S and 6S. Whatever you do now is obviously largely dependent on what you would expect your partner to have for this sequence
in light of the fact that you are looking at the Queen-Jack of spades.
As you may have guessed from the font, I think the part in bold is interesting. That is because your spade holding means that you know more about partner's hand (specifically that he doesn't have a marginal 2C opener with only 5 spades) than you normally would know when the auction goes this way. Also, so far there is no way that partner can know that you know this, but if part of the message of 5S is "my doubleton spade is VERY strong" then bidding 5S will tell him that you already know he has a sound 2C opener. I do think it makes sense that this is part of what 5S is all about - with a lesser doubleton in spades you might choose 4NT (or something else) as your slam try.
Even if you don't buy the part about 5S suggesting a very strong doubleton spade, let's assume it is true (because it leads to something interesting). Now suppose you bid 5S. Now partner knows that you know that he does not have a marginal 2C opener. Is he supposed to take that information into account in deciding what to do over 5S?
Before you answer that, keep in mind that he knows that you know that he knows that you know that he has a sound 2C opening
Perhaps the answer is you should just bid 6S yourself.
Fred Gitelman
Bridge Base Inc.
www.bridgebase.com
PS The above post was not really meant to be taken seriously and it may not make any sense at all. Please keep that in mind before you spend a great of time twisting your brain in knots thinking about this!