Cyberyeti, on 2015-November-15, 10:15, said:
Missing the point, partner needs to know you have the K♠, 6 is not good without it (although it's not terrible) but you certainly don't want to be in a grand without it. 6♣ over 5♦ would absolutely deny K♠ in my book and would be what you would do with ♣AKx or AKQ. 5♠ is a cue with hearts agreed not a signoff.
You are right that 5S is the correct bid, however you are missing the point that if you try for a grand in a suit your partner has denied a control in, you automatically are known to have the ace of that suit. So 5S guarantees the CA also, not just a club control. The reason should be obvious, you cannot be off a first round control of a suit and make a grand so you shouldn't try for a grand when you are known to be off a first round control of a suit. Your suggested auction of bidding 5N over 5S means you need something more, probably a 5th heart or the HQ. That seems like how one would bid with AQJxx AKxxx A xx over 5S. In a perfect world you could stop in 6 opposite 3424 and get there opposite 3433, I'm sure theres enough room and we have 5N, 6C, and 6D all available, but in real life I would just bid 7H over 5S, and if I needed a 5th trump or the HQ that's what I'd bid 5N with (which is generally what 5N in these auctions is used for).
@Kurt: I am all about practical bridge but having bid 4H, you cannot be attempting to sign off in 5S. If you wanted to play spades then don't bid 4H. It is still possible that opener wants to play spades and bid 3H, but it is possible he wants to play hearts also so your signoff has to be 5H (and if partner wants to play spades he can go back to 5S over that). So yeah, 5S is definitely a cuebid even with no agreements, it is just bridge logic.