Probability Distribution of random variable X.

I need help. I am trying to find the Probability Distribution of random variable X. X is the score of an test. In a multiple choice test of 10 questions with k possible answers (only one is correct). Each correct answers is worth five points. There are no penalties for wrong answers. I know it needs to be the Binomial distribution but what is throwing me off is that the random variable X is the score and not the number of correct answers, even though the two are related. Any idea on how to set this up? I tried $\displaystyle P(X=x)= (n choose x) (1/k)^x(1-(1/k)^{(n-x)}$ but I don't think that accounts for everything.