If $\begin{bmatrix} 5x + 8 & 7 \\ y + 3 & 10x + 12 \end{bmatrix} = \begin{bmatrix} 2 & 3y + 1 \\ 5 & 0 \end{bmatrix}$, then the value of $5x + 3y$ is equal to :

When two matrices are equal, their corresponding entries (same row, same column) must be equal.

$\begin{bmatrix} 5x + 8 & 7 \\ y + 3 & 10x + 12 \end{bmatrix} = \begin{bmatrix} 2 & 3y + 1 \\ 5 & 0 \end{bmatrix}$

This gives us four equations:

$5x + 8 = 2 \quad\cdots(1)$

$7 = 3y + 1 \quad\cdots(2)$

$y + 3 = 5 \quad\cdots(3)$

$10x + 12 = 0 \quad\cdots(4)$

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From equation $(1)$:

$5x + 8 = 2$

$5x = -6$

$x = -\dfrac{6}{5}$

Verifying with equation $(4)$:

$10\left(-\dfrac{6}{5}\right) + 12 = -12 + 12 = 0 \;\checkmark$

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From equation $(3)$:

$y + 3 = 5$

$y = 2$

Verifying with equation $(2)$:

$3(2) + 1 = 7 \;\checkmark$

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Now substituting $x = -\dfrac{6}{5}$ and $y = 2$ into $5x + 3y$:

$5x + 3y = 5\left(-\dfrac{6}{5}\right) + 3(2)$

$= -6 + 6$

$= \boxed{0}$