Calculate the distance between points P and T, given the coordinates of the vertices of a cuboid and the positions of P and T.

Here's the solution to the geometry problem:

First, let's establish the coordinates of the vertices of the cuboid and the points P and T.
Let A be at the origin $(0,0,0)$.
Given: $AB = 8$ cm, $BC = 6$ cm, $AE = 5$ cm.
The coordinates are:
$A = (0,0,0)$
$B = (8,0,0)$
$C = (8,6,0)$
$D = (0,6,0)$
$E = (0,0,5)$
$F = (8,0,5)$
$G = (8,6,5)$
$H = (0,6