Yes, boosters typically have short protection. This is more to protect the booster than anything.
Power districts are a personal choice. I have just two guidelines.
1. For HO and smaller, I suggest that modelers have an electronic circuit breaker if they are using an 8 amp booster to make sure 8 amps can't go into a short. That isn't you. You have a 5 amp system.
2. So for you, how many, if any power districts,you have depends on how much "pain" you can stand. This often hinges on how many operators you have. If you are the only operator of your layout, you are likely to know right away when you have a short and even if it takes you several minutes to find, you may not care. So the answer could be, you don't need any electronic circuit breakers.
If you have several operators, you may not want to have your layout completely shut down during an operating session. In this case, you may not be able to stand a lot of pain. You want to get back and operating as quickly as possible. You might want an electronic circuit breaker for every town to narrow your focus when a train stops running.
Hope this helps.
Wiring for DCC