The hosts took 73.4 overs to bowl out Kerala after opting to field at the the picturesque HPCA Stadium. Sanju Samson (30), Raiphi Gomez (32) and Basil Thampi (32) were the contributors to the modest first innings total.
It was Dhawan's second five-wicket haul of the season.
Himachal were 11 for no loss at stumps with Ankush Bains (10) and Varun Sharma (1) in the middle.
Brief scores: Kerala 196 (Sanju Samson 30, Raiphi Gomez 32 and Basil Thampi 32; Rishi Dhawan 5/57, Bipul Sharma 3/37) HP 11/0.