The gradient of a line that is perpendicular to the line described by the equation $y = -x + 5$ is $1$.

To find the gradient of a line that is perpendicular to a given line, we first need to identify the gradient of the original line. The equation $y = -x + 5$ is presented in the slope-intercept form $y = mx + c$, where $m$ denotes the gradient. In this instance, the gradient $m$ is $-1$.

Perpendicular lines have gradients that are negative reciprocals of one another. The negative reciprocal of a gradient can be determined by flipping the number and changing its sign. For the gradient $-1$, the reciprocal is $1$ (since flipping $-1$ gives $1$, and changing the sign results in $1$).

Thus, the gradient of a line perpendicular to $y = -x + 5$ is indeed $1$. This implies that if you were to draw a line with a gradient of $1$, it would intersect the original line at a right angle (specifically, $90$ degrees). Understanding this concept is essential in geometry and is useful for solving various problems involving perpendicular lines.