Adding fan to shower venting question

Im redoing the shower in master bedroom and being there was no ventilation I added a light / fan. I know the fan needs to be vented and its recommended to vent through the roof. We just had the roof redone, so Im not thrilled about having to cut a hole for the vent.

However, there is a dryer venting tube about 3 feet away and I was wondering if I can connect the shower fan vent tubing to the dryer vent tube?

Any potential problems or issues in doing this? Appreciate any advise or feedback. Thanks.

Adding fan to shower venting question