To solve for the point of intersection of the two equations \(y = -2x + 3\) and \(y = 5x + 10\), we set them equal to find \(x\):
\[ -2x + 3 = 5x + 10 \]
Now, let's solve for \(x\):
- Add \(2x\) to both sides:
\[ 3 = 7x + 10 \]
- Subtract 10 from both sides:
\[ -7 = 7x \]
- Divide by 7:
\[ x = -1 \]
Now substitute \(x = -1\) back into one of the equations to find \(y\). Let's use \(y = 5x + 10\):
\[ y = 5(-1) + 10 = -5 + 10 = 5 \]
So, the point of intersection (solution to the system) is \((-1, 5)\).
Based on the choices provided, the answer is:
D. (-1, 5)