I too have to question what a 34 or 35mm tube would accomplish for you? It has close to 28mil if travel already.
Supposably it will let in more light. I say it does but not enough to notice. So i am not all about this advantage.
It does help with having more surface area for yours rings. It would help more towards magnum calibers probably.
I also like having heavier scopes so this will help in the weight department. The mark 5hd is on the light side of things though. The gen ii 4.5-27x56 and like some schmidt and bender scopes they're pretty heavy.
There are also a ton of 34mm rings out there now to buy. There is also a decent amount of 35mm rings out there too now.
But my biggest reason for me is cause of how many 34mm and 35mm scope mounts i have.