East's cue bid promises spade support and at least limit raise values, and not just a strong hand. West has choices, but the simplest is simply to launch 1430 Roman Keycard Blackwood with such a powerful playing hand. Otherwise, the choice would be between 4♣ and 4♦, depending on whether the expectation at this point is control bidding or source of tricks bidding. To avoid any confusion, and without a sense that either method would serve any purpose at all, just ask for the information you need -- aces?

The 5♦ 1430 response shows 0/3 key cards, and while West hopes, prays, and expects three to be the number, there is a delicate agreement that is in play -- with 0 key cards, East may pass and avert an embarrassing result, but when the higher of the "ambiguous" 0/3 is held, it is required to bid on. Holding true to the method develops firm partnership confidence, and West therefore bids 5♠, "pass or correct to slam," and is rewarded when East dutifully carries on.

Good job.