Please help on how to change state if my newbie teleport expired, my base still level 5.?

Without the newbie teleport you cannot change state until you reach level 10 and the State immigration event opens for the state you are in. If its a new state this may take a few months.

State immigration also will cost you money to buy tickets and will restrict where you can move to.

The easier solution at level 5 is to abandon the base and start a new game. It will only take a few hours of playing to get back to level 5 and you will be able to move to any state that you want for free as long as you do it quickly.