To determine the relationship between $|-5|$ and $-|-5|$, evaluate each expression separately. On the left side, the absolute value of $-5$ is $5$, because its distance from zero is $5$. On the right side, evaluate the absolute value first to get $5$, and then apply the external negative sign, resulting in $-5$. Comparing these two integers, the positive value $5$ is strictly greater than the negative value $-5$ ($5 > -5$). By substituting the simplified integers with the original expressions, the final relationship is $|-5| > -|-5|$.