We use the equation of motion:

\(s = ut + \frac{1}{2} a t^2\)

where \(s = -5\) m (since it ends 5 m below the starting point), \(u = 24\) m/s, and \(a = -10\) m/s² (acceleration due to gravity).

Substituting the values, we get:

\(-5 = 24t - 5t^2\)

Rearranging gives the quadratic equation:

\(5t^2 - 24t - 5 = 0\)

Solving this quadratic equation using the quadratic formula \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 5\), \(b = -24\), and \(c = -5\), we find:

\(t = 5\)

Thus, the time from projection until P reaches the ground is 5 seconds.