This is the best time to visit Spiti. This is real peak season in Spiti when the valley welcome hordes of tourists who wish to get respite from city heat. Most of the road links by the mid-June get opened and thus sightseeing in and around Spiti is possible. All the hotel also now offer complete facilities. A visit to Chandra tal can also be made.
Hi poonam May is peak summer and it'll be too hot and you won't be able to njoyy the weather and the landscape..
July to September is the best time. ps : this suggestion is if you want to njoyy Himalayas in its natural form. weather will be reasonable if u don't want to experience that now and cold weather