Microsoft Excel is WRONG!!! Beware...
Sorry, gerdb - you'll have to write to that Doc of yours...
I was schooled in the U.S. and Britain and have tutored and taught math from grade school through college. All I've said adheres to standards of mathematics printed in all levels of books I've ever seen. And yes it's nerdy - but I've seen a bunch of these books because I collect them.
As for other programs, try out Mathematica on this website. Would you think they would have it wrong? Type in -5^2 and you get the correct -25. Try MathCad, or any other program that actually follows math rules and you'll find the same thing, to wit:
-5^2 = -25
-(5)^2 = -25
-(5^2) = -25
(-5)^2 = 25
As for writing out the plusses and minuses, the easiest way to always get this right (from years of teaching this) is to remember the following: Subtraction is just adding a negative and a negative is simply a number multiplied by -1. To use your example:
+5^2 + (-1)*5^2 = 0 is the same as saying 5^2 - 5^2 = 0
(-1)*5^2 + 5^2 = 0 is the same as saying -5^2 + 5^2 = 0
Since, in the order of operations, exponents come before multiplication, you would do the 5^2 first, then multiply by the -1.
All Microsoft tried to do was help reduce keystrokes in formulas. The correct way to get a positive from this is as above: (-5)^2 where the -1 and the 5 are both squared. They just tried to save you the parenthesis.
All I ask is that you spread the word to other engineers. Luckily, I knew that the answer coming through on my spreadsheet was wrong and took the time to find it. What worries me are those that got an answer that was only 5% or 10% off and passed the back of the envelope test, but is now an undersized <> in public use.