Answer
$f=-10cm$
Work Step by Step
Use the lens equation $$\frac{1}{f}=\frac{1}{i}+\frac{1}{p}$$ to solve for $f$. $$\frac{1}{f}=\frac{p}{ip}+\frac{i}{ip}$$ $$\frac{1}{f}=\frac{p+i}{ip}$$ $$f=\frac{ip}{i+p}$$Substituting known values of $p=10cm$ and $i=-5.0cm$ yields an image distance of $$i=\frac{(-5.0cm)(10cm)}{10.cm-5.0cm}=-10cm$$
