You are only allowed to switch clubs in your bag before you start a round. Once you start a round you are stuck with whatever is in your bag.
If you are not in a round try un equiping all your 5 optional clubs on the left hand side by dragging the exisiting clubs out of their inventory slot. Once you have 5 empty slots, drag and drop the clubs you want into your bag slots.
If this does not work, please give me more details on what you are doing and what browser you are using.