Answer
$(x+5+y)(x^2+10x+25-xy-5y+y^2$)
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of two cubes, then,
\begin{array}{l}
(x+5)^3+y^3
\\=
[(x+5)+(y)][(x+5)^2-(x+5)(y)+(y)^2]
\\=
[x+5+y][(x^2+10x+25)-xy-5y+y^2]
\\=
(x+5+y)(x^2+10x+25-xy-5y+y^2)
.\end{array}