It's possible for 2 + 2 = 5 if you change standard conventions.
If you assume a false proposition, you can deduce anything from it and make it true, for one, so it's logically admissible to say "all cows fly, therefore 2 + 2 = 5".
Also, you can change the meaning of the symbols 2, +, = and 5 so they represent things that will make the statement true. For example, let = be still =, let 2 still be 2, let + mean / and let 5 mean 1. I shouldn't need to say there are an infinity of ways to do this.
Finally, you can suppose it's admissible to divide by cero in some system, which would mean you're allowed to say 1 = 0, so it's easy to deduce that 2 + 2 = 5.
Had fun yet? Unless you can do something useful with 2 + 2 = 5, it's kinda silly to try and force it to be that way. Oh, and by the way, this is a maths question, I don't think physics can answer it.
I'm studying to become a mathematician.