I think there is a train, there are also cheap flights from Air Asia.

Chiang Mai is nice. Normally 5 days will be more then enough. Two days for trekking, one day around the city, and one day for temple on the hill and elephant camp, leaves you still a spare day!

You can also, especially if you are not found of trekking, do the golden triangle and also go to Chiang Rai!

Enough possibilities to fill your 5 days!