Question 1185100
It is a result in statistics, which you should also be aware of because you were given this kind of problem, 
that if X ~ N({{{mu[1]}}}, {{{sigma[1]^2}}}) and Y ~ N({{{mu[2]}}}, {{{sigma[2]^2}}}), and X and Y are independent from each other, then 

X - Y ~ N({{{mu[1]-mu[2]}}}, {{{sigma[1]^2 + sigma[2]^2}}}).

Since the two scores were sampled randomly from the same population, the scores are independent from each other, and so 

X - Y ~ N(0, {{{ 10^2+10^2 = 200}}})


===> {{{P(X-Y > 5) = 0.362}}} 


Normal probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.