More Dice.........

[n + n^2 + n^3 + n^4 + n^5 + n^6]^15.

The expansion of this generating series will give terms from n^90 to n^15. You simply calculate the coeffficient of n^53 =27,981,391,815. Then 27,981,391,815 / 6^15=0.059511.... x 100 =5.9511%, which is the exact probability.

Why do you think that this is true?  It makes no sense to me.

http://www.wolframalpha.com/input/?i=15+tosses+of+6-sided+dice,+total+of+53