It depends if they have any spaces and what their admission criteria are. It is the LEA who handles applications normally but the school will be able to tell you info on numbers. If you apply and get rejected, you can appeal. If you can prove that the disadvantage to your child not attending outweighs the disadvantage to the school of having to accept one more pupil, you can win at appeal. If you don't appeal (or don't win your appeal) you might be near the top of the waiting list because of your proximity to the school if that is used as criteria. Many faith schools however give priority to children who are regular worshippers (and require proof of this) in which case living nearby may not be an advantage unless you can also prove church attendance. You really need to look at their admission policy and see what it says.
Once you move into the area the LA will have to find you a place somewhere. If the CofE school has a place you will be admitted - they don't have any choice in that. However, if the CofE school is full the LA will offer you the nearest school with places available. If all the schools in the area are full they will offer you the nearest school that is best able to cope with an additional pupil. That may be the CofE school but it may be somewhere else.
As we are talking about Y5 there is unlikely to be much of a waiting list if there is one at all. Your position on the list depends on the school's admission criteria. You can go down the list as well as up - another child moving into the area and qualifying under a higher admission category will go ahead of your son on the waiting list.
If you are refused entry to this school you can appeal. Any appeal will be about the balance of prejudice as HushedTones describes.