\( -5=-|c-5|+3 \) he solution set is \( \square \)

To solve the equation \( -5 = -|c-5| + 3 \), we first isolate the absolute value term: \[ -5 - 3 = -|c-5| \] \[ -8 = -|c-5| \] Now, multiplying through by -1 gives: \[ |c-5| = 8 \] This absolute value equation means \(c-5\) can equal 8 or -8, so we can set up two equations: 1. \( c - 5 = 8 \) leads to \( c = 13 \). 2. \( c - 5 = -8 \) leads to \( c = -3 \). Thus, the solution set is \(\{ -3, 13 \}\).