DOB's answer seems fine except that if you use ln e then it's possible to express 5 using only one 2 (for it can be written as 2 + ln e + ln e + ln e. In fact, it can be written without using a 2 at all).
There are also various other ways of making up the extra 1. For example, (sin x)squared + (cos x)squared + 2 x 2 = 5.
Or, negative e to the power of i times pi + 2 x 2 = 5.
Finally, how about [e squared] - 2 = 5 where the brackets [ ] indicate that you take the greatest possible integer below e squared (this is standard mathematical notation and perfectly acceptable).