I like the double. It is an anticipatory double. Lead back the first suit bid in dummy.
As to what to lead. Lead a diamond like partner asked.
Seriously, this is interesting. In theory, partner cannot expect that your request for a diamond back is based upon the Kx, as that would be stupid. He also cannot expect that it requests a lead back from Ax, as you could probably find that lead yourself. AQ is wrong for a number of reasons. So, the X, if partner is atune to the thinking here, should show a void.
Making that assumption, it would make little sense for a double of 5
♦ to request the lead of the void. Rather, the double should suggest that partner does, in fact, want you to lead whichever black suit the double of 5
♦ flags.
That's the BIG question. What would be the meaning of a double (and hence the inference from a non-double) in this scenario. Or, what is an immediate double of 5
♦, as opposed to, perhaps, a late double of 5/6
♥?
This is perhaps where a little bit of a default agreement works. My instincts tell me that I should lead a club if I had to guess. Why? Most doubles tend to look downward rather than upward, it seems. I double because I cannot any longer bid the suit I wanted to bid. I double because they have stolen my ability to bid. I double because they preempted me. This of course makes no direct sense here, as partner would not bid 5
♠ for a spade lead, but consistency of thought suggests that the double asks for a club because "I could bid 5
♠." The pass, then, would ever-so-slightly push me toward spades, bolstered substantially if partner makes a late double.
So, I lead a club.
"Gibberish in, gibberish out. A trial judge, three sets of lawyers, and now three appellate judges cannot agree on what this law means. And we ask police officers, prosecutors, defense lawyers, and citizens to enforce or abide by it? The legislature continues to write unreadable statutes. Gibberish should not be enforced as law."
-P.J. Painter.