Answer
$y^6-6y^5r+15y^4r^2-20y^3r^3+15y^2r^4-6yr^5+r^6$
Work Step by Step
Using the coefficients in the $r=5$ row of the Pascal's triangle, $\left\{
1,6,15,20,15,6,1
\right\}$, and the pattern in expanding binomials, then $
(y-r)^6
$ expands to
\begin{array}{l}
y^6-6y^5r+15y^4r^2-20y^3r^3+15y^2r^4-6yr^5+r^6
.\end{array}
