Changing Pressures and High Altitude OK 5 Weeks After Rhinoplasty?

Of course you should check with your surgeon. I would be worried about the mild loss of sensation that occurs in the tip of the nose after rhinoplasty. In the high altitude, very cold conditions of Everest you are at high risk of frost bite. You might not be able to tell that you are having a problem until it is too late. Here is a link to the story of Beck Weathers who lost his nose during a climb that went bad.
http://www.kepplerspeakers.com/speakers.aspx?name=Beck+Weathers,+MD
I am not really worried about pressure chages at 6 weeks-your nose should be healed enough.
I wish you luck and success with your climb.

 I have all of my patients take Afrin with them if they are going to altitude just in case they are not able to clear their ears or sinuses on the descent. No problem on the ascent.

You should ask your surgeon for specific advice regarding your surgery and your situation. The main concern with strenouos activity after Rhinoplasty Surgery is a nose bleed. I will usually allow my patients to resume unrestricted activity 3 weeks after nose job surgery. Again, it is best to check with your surgeon for this specific recommendation.
I hope this is helpful for you.