You should explore Meghalaya especially Cherapunji where you can find nature at its best along with several waterfalls. it can also be covered within 5 days.
North east sikkim Lachung and Lachen will be best for you. If you want to explore more of north east, you can have a look to this informative video I found on youtube https://youtu.be/iCNE-aI05PY
Himachal Pradesh is one of the best place that you could visit.Kulu,Manali and other famous tourist destinations are waiting for your arrival to surprise you with their delightful and enriching nature and other eye blinding experiences.So this would be a great choice.But you could extend your 5 days a little more i think so.But uf you can travel in airplane then i think it would be fine othervise travelling would steal much of your time.
I also visited north east last year in summers so i would suggest u to visit..
1. Nathula paas
2. Takdah in Darjeeling ( it's a must visit place - a sort of town with bungalows made during colonial period)
3. Places in North sikkim
Within five days time Meghalaya will be best option. Spend two days in Shillong, two days in Sohra (Cherrapunji) exploring waterfalls and hiking, and one day visit to Mawlynnong (cleanest village) and Dawki river. Meghalaya Tourism Department runs many day tours from Shillong covering these places. Here is an interesting link on things to do in Shillong. Happy traveling! https://mastmusaphir.wordpress.com/2019/02/16/10-things-to-do-in-shillong/