$$5\cdot(3-x)+8x = 3(x+5)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 5\cdot(3-x)+8x &= 3(x+5)&& \text{simplify left and right hand side} \\[1 em]15-5x+8x &= 3x+15&& \\[1 em]3x+15 &= 3x+15&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 15 }$ to the right} \\[1 em]3x-3x &= 15-15&& \text{simplify left and right hand side} \\[1 em]3x-3x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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