smc

Plugging in the x and y values, we obtain the following system of equations: $$\{\begin{array}{l}1=a-b\\ 5=a-\frac{b}{5}\end{array}$$ We can then subtract the equations to obtain the equation $4=0.8b$, which works out to $b=5$. Plugging that in to the original system of equations: $$\{\begin{array}{l}1=a-5\\ 5=a-\frac{5}{5}\end{array}$$ It is easy to see that $a=6$, and that $a+b$ is $\boxed{11}$.