Nepal with Annapurna trek would require at least 2 weeks. Bhutan can be done in 4-7 days. Tibet 4-7 days (if not going overland one or both ways - would add a few days), India, if only Delhi 3 days, if Agra, etc, 10 days, if other places a lifetime.
With 5 weeks I suggest flying into Delhi, do Tibet, Nepal, and back to Delhi. That works well with flights. Spend the bulk of your time in Nepal. You can do a Tiber sidetrip from Kathmandu easily without pre-booking. Flights KTM-DEL are very cheap so you can play it by ear once you hit Nepal.