Great project… good luck for the backpack in China, it’s a quite “tough” country to backpack, but not impossible… especially if you do it after 5 months of learning mandarin, it will be very useful.
5 weeks seems a bit short to combine these 3 countries, China & India are large countries and transportation may take hours/days, moreover you will be starting from the middle… country. I’ll recommend you focus on China & Japan or China&India. From Guilin you can go to Shenzhen/HK, then maybe Taipei, or directly to Shanghai, then fly to Tokyo/Osaka, etc…