1. The problem is to show that the lines $L_1$ and $L_2$ are parallel. 2. The equation of line $L_1$ is given as $$y = 5x + 1,$$ which is in slope-intercept form $y = mx + b$ where $m$ is the slope. Here, the slope of $L_1$ is $5$. 3. The equation of line $L_2$ is given as $$2y - 10x + 3 = 0.$$ 4. Rearrange $L_2$'s equation to slope-intercept form $y = mx + b$: $$2y = 10x - 3$$ $$y = \frac{10x - 3}{2} = 5x - \frac{3}{2}.$$ So the slope of $L_2$ is also $5$. 5. Since both lines have the same slope $5$ but different intercepts, they are parallel lines. **Final answer:** Since the slopes of $L_1$ and $L_2$ are equal ($5$), the lines are parallel.