Given here: Focal length of convex lens, $f=10 \mathrm{cm}$

Now, as seen in figure, image from lens is formed at point $I_1$, whose location is $5 \mathrm{cm}$ from mirror. Thus, $I_1$ is at $15 \mathrm{cm}$ from lens.

Using lens equation, we have

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Putting the value, 

$\frac{1}{15}-\frac{1}{-u}=\frac{1}{10}$

$$\begin{gathered} \Rightarrow \frac{1}{u}=\frac{1}{10}-\frac{1}{15} \\ \Rightarrow u=\frac{10\times 15}{10-15} \end{gathered}$$

Thus, object is placed at $30 \mathrm{cm}$ from lens.