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I really hope some of the Local Guides have experience and give good advice on doing this trip.
My personal experience, as I have lived three years in China, is check out all the transport you need to take - fast/slow trains, the time that you will need to reach some specific places. If you have 5 days and you are arriving on day 1 at Chengdu and you are leaving on day 5 from Chengdu back home with an airplane. This would mean that you have 3 days left. Day 2 is to reach out the Mount Siguniang National Park, find a place to sleep somewhere near the mountain. Day 3 climb the mountain and enjoy your time there. Day 4 be sure to head back to Chengdu.
P.S.: I have also heard that there is a very big national park in Sichuan province where wild pandas live, maybe if it is on the way, you can visit it too.
To my knowledge foreigners are always required when entering Tibet to have permit.
What’s more foreigners for sure cannot enter on their own (alone) Tibet Autonomous Region, they must be accompanied by a tourist guide and go there with a group. Also keep in mind there are some restrictions which include foreigners of some countries are not allowed to enter that region.
I guess you must double-check the above information and see all the requirements.
Hope you can make it out there and share with all the Local Guides your amazing experience there!