North Sikkim will still be cold in May, so pack accordingly. Don't miss Kala pathar and Katao, very beautiful places and not too crowded. Along with famous tourist places like lachen, Lachung and Yumthang, try to visit Dzongu and Mangan and stay in homestays.
Ask a private cab or shared taxi from Gangtok; roads are winding, so start early each day.
Permits required: Protected Area Permits (PAP) for North Sikkim, your hotel or cab driver can arrange them.
Altitude caution: Gurudongmar Lake (17,800 ft) is high; acclimatize in Lachen for a day, carry warm clothes.