What we’re looking for is the value of k that will satisfy the equation.
The solution would be like this for this specific problem:
5k =1 (mod 26)
Check how 5*5 = 25 = -1 (mod 26)
In this way, 5*(-5) = -5*5 = -25 = -(-1) = 1 (mod 26)
Thus, k = -5 = 21 (mod 26)
And 5^-1 = 21 (mod 26)
I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.