I'll need to leave my bag either in Phuket or in Malaysia KL for a few months, around 3-5. First my question is about Phuket: where can I leave it for that long and approximately how much will it be?

I think you need to be a bit more specific about the bag (LxWxH and weight) to get a better estimated price

Good Luck

Whats in the bag

There is a self storage place next to JungCeylon in Patong. Just google "storage in Phuket".

Make good friends with your local laundry lady. Let her look through the bag, and she'll probably store it for a song and dance. A few hundred Baht at most.

20-30 kg bag, clothes and other stuff inside.

Depending on where and how long you are staying now, just ask the reception. Many guesthouses will keep your stuff, while you are away. It is for them like a guarantee you come back as a customer...