If it's the Sheraton on Huajin Road, that's reasonably close to the airport. I should think a taxi to hotel would only be about RMB 30-ish. You can see the huge premium the hotel is charging.
Five full days 21-25 is quite a long time for Chengdu city and environs. I'd suggest Giant Panda Breeding Center of course (go first thing in morning), one or more of the large parks and a bit of teahouse visiting, Wenshu Temple in center of town. North suburbs and beyond: Sanxingdui Museum (in Guanghan city) and Baoguang Temple. West of Chengdu--Dujiangyan Irrigation System. All of this plus some city filler sights can be done in about 2.5 days. Consider going somewhat farther afield to Leshan (Giant Buddha) and maybe an old town like Luocheng or Shangli. Emei Shan if you are interested in Buddhist Mountains, don't mind climbing a lot of steps, and have at least one day of favorable forecast. Usually a Leshan-Emei Shan trip will be at least one overnight outside of Chengdu. Yet another option, if you don't mind spending the cash, is to go to Jiuzhaigou and Huanglong in the mountains, which at the time you're going (assuming October) is peak fall foliage season. You'd need to fly up and back ex-Chengdu and it would take 3 days/2 nights including the travel days. There is a Sheraton near JZG park entrance but it's possibly sold out by now.
IMO, staying this entire time in Chengdu city is a waste of good opportunity, if you aren't working the sightseeing around business commitments and your time is completely flexible.