The beauty of making an opening preemptive bid is that your job is now done. You've described your hand, and the rest is up to your partner ...
... who is you on this hand. Your partner opened 3♦ and East (after a bit of humming and hawing) has finally bid 3♠. What's the first thing you do? And the next thing you do? And finally, what do you bid?
The first thing you do is check the vulnerability, which tells you that a sacrifice will be CHEAP (because you're not vulnerable) and letting them make game will be EXPENSIVE (because they are vulnerable).
Next, you decide whether they're likely to make game in spades. If partner's a weak hand, then surely they are. Easy, then. Your partner got in East's way, and from all the hesitating going on, it almost worked. Now you have to do the same. West is surely going to bid 4♠ anyway, so give her something to think about: raise your partner to 5♦. (You're going to make 7 diamond tricks and with luck partner can provide one more, for 8 tricks. Doubled, that'll cost you 500, which is at least 120 cheaper than them making game in spades. Cheap at the price!)
If West doubles you for penalties, you're home and dry: if you can go just 3 off, you're showing a profit. But one more question for you:
Supposing West instead raises her partner to 5♠. North and East will pass and it's your bid: do you now go on to 6♦?
Don't even think about it. For one thing, that's going to cost you 800, which is MORE than they can make for game in spades. But there's another, much stronger reason. We just agreed, didn't we, that your partner might have just one trick outside diamonds. OK, that's one trick. The only possibility for a second is your ♦A and you already know that you can't make a trick with that. Don't you? If partner has 7 diamonds for her opening preempt and you have 5, the opposition only have one diamond between them. So they're going to ruff diamonds from trick one. In other words, EW have probably got a small slam in spades. And the only way they're going to bid it is if you force them up by bidding 6♦. So 6♦ is a disaster, whether NS bid on or not.
Have a look at the whole deal and you'll see that EW do indeed have a small slam in spades. Thank goodness, then, that you left them to make their 5♠. But why, you may ask, did we bother with all that preempting? Didn't help in the end, did it? Well, it might have, for three reasons:
1 There will be Easts who, with just 8 points and missing the ♠AKQ, will be put off bidding at all, in which case your 5♦ will certainly silence West.
2 And if East does bid 3♠, there will certainly be Wests who will prefer to double 5♦ for a sure penalty than raise partner to what may well be a dodgy 5♠.
3 And even if they bid and make 5♠, you might well have put them off looking for what turns out to be a stone cold slam in spades OR clubs.
In Box & Bath
In Bath, 4 pairs reached 5♠ and 4 pairs played in 5♦X. Fine. The other three results were substandard: one EW was allowed to play in 4♠ (S didn't raise to 5♦), one NS played in 5♦ UNdoubled (see below) and one NS went the extra step too far into 6♦X, which duly cost 800.
In Box, we had one pair in 5♠ and three in 5♦. So far, so good. But NONE of the 5♦ contracts was doubled. You got the preempting right, but when you know an opponent is making a sacrifice you HAVE TO DOUBLE IT. Otherwise, they're laughing all the way to the bank.