1. The problem asks for the equation of a straight line passing through the point $(1, 5)$ and parallel to the line $y = -2x + 3$. 2. Recall that parallel lines have the same slope. The given line has slope $m = -2$. 3. Use the point-slope form formula for a line: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is the point the line passes through and $m$ is the slope. 4. Substitute $m = -2$, $x_1 = 1$, and $y_1 = 5$ into the formula: $$y - 5 = -2(x - 1)$$ 5. Simplify the right side: $$y - 5 = -2x + 2$$ 6. Add 5 to both sides to solve for $y$: $$y = -2x + 2 + 5$$ $$y = -2x + 7$$ 7. The equation of the line in slope-intercept form is: $$y = -2x + 7$$