Take the bus, really easy. You will load a baggage cart, exit Customs, buy your bus ticket, wheel your cart to the numbered bus platform where bus staff will take it from you and give you a claim check. They will load it underneath when the bus arrives as the passenger climb up and aboard. Same thing in reverse upon arrival and there will be carts waiting at the arrivals drop-off point. If had to transfer between any two terminals in the world with my luggage like this I would absolutely choose these two. Have done it in my sleep, well almost By the way, also going to BKK.