Why do you want to do an extra A-level? From the fact that you don't want to do General Studies and Critical Thinking because "they're aren't accepted everywhere", it shows that this has something to do with university applications.
YOU DO NOT NEED 5 A-LEVELS.
I can understand the reason why you are taking the A-level as a private candidate, your college has rightly refused for you to do a fifth A-level. Of course many people do 5 A-Levels and get good grades in them, but you're better off devoting your time in getting the highest grades possible in your four A-levels.
Judging by your A-level subjects and the motive that you have in doing a fifth 5 A-Level, will you be applying for Medicine this year?
(Or a subject allied to Medicine).
Remember, it's not all about grades for Medicine.
Definitely not. If you think you're going to have an advantage by doing a fifth A-level, well, I sincerely doubt that. Many do 3 A-levels and get into Medicine just fine.
You would also be doing it in Year 13. To do 5A2s and 1AS (as you'll be taking the full A-level) is not worth it as you may fail to make any offers (and they will not stipulate a 5 A-level offer. This may have been done one or twice for Cambridge entry, but that's about it).
Ridiculous. Forget about it. You're grasping for straws if you think an extra A-level will help your application for Medicine. Damn ****ing not.