functions - Is 4.99999......... exactly equal to 5?

I'm a student of 10th std. Recently our teacher asked a Question that

"Is 4.999...equal to 5 or not?" Everyone said that is isn't equal or it is approximately equal. Teacher too agreed to that. But I did't agree. I opposed the teacher as I think it is precisely equal to 5. I also prove but then too she isn't satisfied. Can you please explain what is right and what is wrong in this case?Please Justify.

   Proof that I showed : let x=4.999...  (a)
                           therefore, 10x = 49.999...
                                      10x -x = 49.999... -4.999...
                                      9x     =  45
                                      x = 45%9
                                      X= 5     (b)
                         hence (a) =(b).
                                    And therefore, ***4.999... = 5***