That's a tough one.
Layang Layang in May offers the potential for seeing the migrating hammerheads. Absolutely thrilling. And the place is so remote with such deep walls that it's pretty much a magnet for marine life. Very rich. If it ends up being June, you may miss the hammers, but the rest of the diving is still going to be very good.
Raja Ampat in May is also excellent. I would recommend a liveaboard, or if land-based, going to the northern area rather than the southern area. The mantas and the wobbegongs are in the north. In June the boats will be relocating to Komodo, so your selection of liveaboards would be greatly diminished.
Tubbataha is really seasonal and the season ends in June, so again, May is a good time to go. Boats fill up fast, though, and tend to be rather expensive for what you get. I wouldn't worry even one minute about that travel advisory--it's for a different part of the country. And I wouldn't worry about the warship having run aground--the boats you'd be on wouldn't be US-registered and the Philippine Navy won't care about the nationality of dive boat passengers.
If you were my customer, I'd need more information than what you've given (just the month) in order to guide your choice. I'd have to know about your budget, your creature-comfort expectations, your dive history, etc.