(y+5)^3 is the same as (y+5)(y+5)(y+5)
It is easiest to multipy out 2 of the brackets first
(y+5)(y+5)
y^2+5y+5y+25
y^2+10y+25
We then have to multiply what we just got by (y+5). I personally multiply it all by y first to get
y^3+10y^2+25y
and then multiply the first answer by 5 to get
5y^2+50y+125
then add these together for the final answer
y^3+15y^2+75y+125