E/All		♠	A J 6 4 3
		♥	A J 10 2
		♦	Q 5 4
		♣	9
		♠	9
		♥	K Q 9 3
		♦	A K J
		♣	A J 6 5 2

¹ Forcing (highly recommended!)

South has never been accused of underbidding...

Aside: instead of 4NT (Blackwood), a much better bid would have been 4♣ (control showing), since North could have been somewhat weaker than he is. North then bids 4♠ (control showing, accepting the slam invitation). Now is the time for South to apply Blackwood and over the 5♥ response he makes a grand slam try: 5NT. This way South informs North that the grand may be on but that something extra in North is needed. (Opinions differ about how to respond to 5NT, this is a matter of partnership agreement).
North has shown all there is to show (except his singleton club but that is often not an asset, since it is in South's first suit, which is at least a five card suit), therefore he signs-off, meaning the contract will be 6♥. Much better bidding than this regrettable 'standard-direct-Blackwood-bidding'...

But none of that matters; South is in 7♥ and West leads the ♣K.
How should South play?

Solution

Declarer counts four club losers in hand and four spade losers in dummy. If he elects to establish the fifth card in one of the black suits by ruffing, that will succeed if it is 4-3, by ruffing three times (unless the ♣KQ respectively the ♠KQ come down in three rounds, a small chance; in that case two ruffs suffice). After ruffing good the fifth card in that black suit, he has to draw trumps, in order to enjoy that fifth card.
Since there are more entries in the South hand, the obvious choice is to ruff out the clubs.
Here we go: ♣A, club ruff, diamond to the ♦A, second club ruff. Oops:

E/All		♠	A J 6 4 3
		♥	A J 10 2
		♦	Q 5 4
		♣	9
♠	K 10			♠	Q 8 7 5 2
♥	7 4			♥	8 6 5
♦	10 7 3 2			♦	9 8 6
♣	K Q 10 7 4			♣	8 3
		♠	9
		♥	K Q 9 3
		♦	A K J
		♣	A J 6 5 2

East discards a diamond and the grand has flown out of the window (just try). Ruffing out the spades would not have helped, that suit is 5-2 as well (by the way, if that suit had been 4-3: can declarer, after having ruffed three spades, still enter dummy in order to draw trumps and cash the fifth spade?).

On closer inspection: there is a better chance: how about South ruffing all of North's spades and North ruffing all of South's clubs? Yes, a cross-ruff.
In a cross-ruff, unlike other trump contracts, it is more practical to count tricks, rather than losers. Indeed declarer can count thirteen tricks: eight ruffs, the black aces and three diamonds.

Since declarer is not going to draw trumps at all, he must cash his tricks in the side suits as quickly as possible. Why? Since during the cross-ruff a situation will occur, in which an opponent is out of the suit that is being ruffed. He will then discard a suit (in this case diamonds), making it impossible for declarer (who will not draw trumps, keep that in mind) to cash all his tricks in that suit, since that opponent will now ruff.
We have seen that happening in the failing line of play earlier: at the moment North scores the second club ruff, East discards a diamond and declarer cannot cash his third diamond trick anymore.
So after winning the lead with the ♣A he cashes three diamonds at once. That suit will have to be 4-3, whereas there is no problem if the black suits are 5-2. In the line of play that failed, both the diamond suit and the black suit which was to be ruffed out, had to be 4-3 (South should have cashed three diamonds first as well): that is why the cross-ruff is superior.
If the three diamond tricks are not ruffed, he sighs in relief. Next he ruffs a club in dummy with a low trump, cashes the ♠A and ruffs a spade with his low trump. If all this succeeds, declarer's worries are over: he has a 'high cross-ruff' left; he wins the last six tricks by cross-ruffing with high trumps. In the end EW will have to underruff.

It will be clear from all this, that West could have defeated the grand by leading a trump.