What Cassette is best for Climbing 4000-5000M Elevations?

The amount of climbing actually doesn’t have that much of an impact on your gear choice, but rather the grade. The grade, combined with your Power/weight will determine your climbing speed and that will determine your gear ratio needed.
With a ride this long, you will likely want to go far below your FTP.
The way I approach Chainring/ cassette choice, is Iook for the the parts where I suspect going the slowest. Usually the longest and steepest climb.

Then I plug my weight, my bikes weight (don’t think weight weenie here, you have water, spares, a pump, food, maybe lights etc on your bike and are likely not naked either), the power I want to go at, the type of bike I am riding, and the grade into this Tool:

It will give you a speed. Say 11kph at 8% at 180W.

With that information in hand.
I go into this tool:

There you can put your tire diameter, your chainrings and your cadence.
You can now play around with different cassettes and see what works.
It is always advisable to have a spare gear, and not be forced to ride at 70 cadence, in your smallest gear, at threshold for prolonged periods of time.
If you have to choose between cassettes, choose the one with the lower gear (so the bigger sprockets). Never have I ever heard anyone arrive at the finish line of an epic mountain FONDO and say „damn, I didn’t find a big enough gear, should have gone for a faster cassette“

I am not terribly unfit and not too heavy either and I am choosing a 1:1 lowest gear or lower for epic Alpine days.

Hope that helps.

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