All the incidents have happened between 6pm and 10pm. Two were on Sunday 27th December 27, two the following day and there was also one on Tuesday 15th December.
An Avon & Somerset police spokesman said: “We believe the same man is responsible. He targets women on their own, two who were sitting in parked cars and three who were out jogging or walking.
“He is aged between 18 and the mid-20s, about 5ft 7in tall and of athletic build. He was wearing dark jogging bottoms with a white stripe or stripes, and a black hoodie. He could be riding a bicycle.”
Anyone who knows a man matching that description, or who has any information, is asked to call 10, quoting reference number 5215063717.