First, your English is far better than my (put pretty much any language here)! But your equation may be wrong: 5^n> 5v- 1 doesn't make sense. Did you mean 5^n> 5n-1?

To prove that using "mathematical induction" you do two things- first verify the statement for n= 1: 5^1= 5> 4= 5(1)- 1. So that's true.

Now prove "if the statement is true for n= k, it is also true for n= k+1.

If 5^k> 5k- 1, and 5> 0, 5^{k+1}> 5(5^k)> 5(5k-1). Now you need to prove thatthat, 5(5k- 1)= 25k- 5, is greater than or equal to 5(k+1)- 1= 5k- 4.