Step 1 :Perform the operation $B+BC$ with the given matrices:
Step 2 :Matrix B is \[\begin{bmatrix} -8 & 10 & 3 \\ 6 & -5 & -3 \end{bmatrix}\]
Step 3 :Matrix C is \[\begin{bmatrix} -5 & 10 \\ 2 & -5 \end{bmatrix}\]
Step 4 :The operation $B+BC$ cannot be performed with the given matrices because the dimensions of $B$ and $C$ are not compatible for multiplication.
Step 5 :\(\boxed{\text{The operation } B+BC \text{ cannot be performed with the given matrices because the dimensions of } B \text{ and } C \text{ are not compatible for multiplication.}}\)