How do I write a vector as a linear combination of other vectors.
So...you've done the hard part, now finish it off:
$$c_1\begin{pmatrix} 1 \\ 2 \\5 \end{pmatrix} + c_2 \begin{pmatrix} 3 \\ -4 \\-1 \end{pmatrix}+ c_3\begin{pmatrix} -1 \\ 1 \\1 \end{pmatrix} = \begin{pmatrix} 5 \\ 3 \\15 \end{pmatrix}$$
So what have you found to be $c_1, c_2, c_3$?
Fill in the correct values for each constant, and you're done!