The given equation is:

$AX + B = C$ where:

$A = \begin{pmatrix} 3 & 0 & 5 \\ 0 & 1 & 3 \\ -1 & 2 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 3 \\ 0 & 1 \\ 2 & -1 \end{pmatrix}, \quad C = \begin{pmatrix} 0 & 3 \\ 2 & -1 \\ 4 & 5 \end{pmatrix}.$

We are tasked with solving for $X$, where $X$ is a matrix.

Steps to solve:

1. Start with the equation: $AX + B = C$

2. Subtract $B$ from both sides: $AX = C - B$

3. Compute $C - B$, then solve for $X$ by multiplying both sides by $A^{-1}$ (the inverse of matrix $A$).

Let me calculate the intermediate steps for you.The solution for the matrix $X$ is:

$X = \begin{pmatrix} -1.5 & 5 \\ -0.1 & 7 \\ 0.7 & -3 \end{pmatrix}$

This matrix satisfies the equation $AX + B = C$.

Would you like any further details or have questions? Here are some related questions for further exploration:

1. How do we calculate the inverse of a matrix?
2. What are the properties of matrix multiplication?
3. Can you solve the system using Gaussian elimination instead of matrix inversion?
4. What conditions make a matrix invertible?
5. How do errors in matrix elements affect the final solution in real-world applications?

Tip: When performing matrix operations, always ensure that the matrix is invertible before calculating the inverse.