how much to rent a van with driver for 5 of us for a day sightseeing trip in Chengdu?

Where do you plan to go?
If you just travel around the city center area, there is no need to hire a van and the local public buses and subways can help you to travel around.
If you want to go to further places, the price is different for different places.
If you want to know some detail information, you can tell me more detail informatino.

Intend to visit Panda Reserve Base, Dujiangyan Irrigation system, huanglongxi ancient town, leshan gian Buddha, Emei shan.

As I know, hiring a van to Leshan costs about 300RMB. To reach Dujiangyan, the fare is around 200RMB from CD.
In my opinion, the buses from CD to Dujiangyan, Leshan and Emeishan are frequent and easy to take, so it is suggested to go there by public bus.
For the Huanglongxi and the Panda Base, you can hire a van. To reach the Panda Base, the fare is around 150RMB for round trip. To Huanglongxi, the fare is around 200 to300RMB for round trip.

Hi, we have 5 adults. Is there a problem taking taxi from airport to Somerset Riverview Chengdu? Are 5 passengers allow in 1 taxi?

Don't worry! Some taxis in Hk can hold 5 passengers. Flag down one with the mark of "with five seats" on the taxi body.