The slope of a line that is parallel to the equation $y = 5x - 3$ is $5$.

In mathematics, the slope of a line measures its steepness and is commonly denoted by the letter $m$. The equation of a line is typically expressed in the form $y = mx + c$, where $m$ represents the slope and $c$ denotes the y-intercept. For the line given by the equation $y = 5x - 3$, the slope $m$ is clearly $5$.

When two lines are parallel, they share the same slope. Therefore, any line that is parallel to $y = 5x - 3$ will also have a slope of $5$. Although the y-intercept (the point at which the line intersects the y-axis) may vary, the steepness of the line remains constant.

Grasping the concepts of parallel lines and their slopes is essential in coordinate geometry. It plays a vital role in solving a variety of problems related to line equations, graphing, and analyzing the relationships among different lines. For instance, if you are provided with a different line equation and tasked with finding a line that is parallel to it, you simply need to ensure that the slope remains the same. This knowledge simplifies the process of writing the equation of the new line, as the only element that may change is the y-intercept.