Perform the multiplication or division and simplify (frac (x^3)/(x+5))((x)/(x^2)+10x+25) square

To simplify the given expression, we need to perform the division and then simplify the resulting expression.<br /><br />The given expression is:<br />$\frac {\frac {x^{3}}{x+5}}{\frac {x}{x^{2}+10x+25}}$<br /><br />Step 1: Rewrite the division as a multiplication by the reciprocal.<br />$\frac {\frac {x^{3}}{x+5}}{\frac {x}{x^{2}+10x+25}} = \frac {x^{3}}{x+5} \cdot \frac {x^{2}+10x+25}{x}$<br /><br />Step 2: Simplify the numerator and denominator.<br />$\frac {x^{3}}{x+5} \cdot \frac {x^{2}+10x+25}{x} = \frac {x^{3} \cdot (x^{2}+10x+25)}{(x+5) \cdot x}$<br /><br />Step 3: Factor the numerator and denominator.<br />$\frac {x^{3} \cdot (x^{2}+10x+25)}{(x+5) \cdot x} = \frac {x^{3} \cdot (x+5)^{2}}{(x+5) \cdot x}$<br /><br />Step 4: Cancel out the common factors.<br />$\frac {x^{3} \cdot (x+5)^{2}}{(x+5) \cdot x} = \frac {x^{2} \cdot (x+5)}{x}$<br /><br />Step 5: Simplify the resulting expression.<br />$\frac {x^{2} \cdot (x+5)}{x} = x \cdot (x+5) = x^{2} + 5x$<br /><br />Therefore, the simplified expression is:<br />$\boxed{x^{2} + 5x}$