Playing 5. h4 d6 6. h5 seems very risky to me. Maybe I'm just not aggressive enough to play such a move, but I would not wanna just sacrifice a pawn when it's not so clear we get a strong attack after that and we haven't even castled yet. I see no reason for us to be hyper aggressive here when our position is completely fine.
After 5. h4 d6 6. h5 Nxh5 7. g4 Nf6 8. g5 Nfd7 9. Be3 c5 I think we'll get into all sorts of trouble. We can't take on c5 or play d5 because of ...Bxc3+ (black gets a check). Black can put more pressure on d4 and trade a bunch of pieces on d4 (and maybe even win the g5-pawn after that) and trading pieces should be good for the defender (black), since he is up a pawn. Not to mention the second event hasn't been started yet, which makes it even more risky.
The idea for black to move the f6-knight and play ...c5 is something that might happen in other lines too and it's something I think we should watch out for.
Playing 5. h4 d6 6. Be2 seems less risky than 5. h4 d6 6. h5, but still a bit too risky for my taste. But I've only looked at a few lines after 5. h4 d6 6. Be2, and not in much detail, so I can't really tell if 5. h4 is good or not. I used opening explorer a bit for the analysis of this line. One possible continuation is 5. h4 d6 6. Be2 c5 7. d5 (maybe 7. Nf3 is playable here; I haven't looked at it) 7...e6 (see analysis board below for more details) and the position might open up a bit. It feels a bit risky for white, especially considering the second event hasn't been started yet.
With 5. Nf3 it kinda feels like we're deciding not to play h4 (since we can't prepare h4 h5 with Be2 or f3 and g4 anymore if we play Nf3), but that might be fine.
5. Be2 is the move I like the most here. It's very flexible. We still have the option of playing h4 if we think it's a good idea (but at the moment I'm skeptical of this).
I've only briefly looked at a few lines, so a lot of the analysis below is probably wrong. The lines below are by no means forced.
I really think that we can play Nf3 after h4 d6 if the calculations don’t work