5. Two particles \(P\) and \(Q\), of masses \(2 m\) and \(3 m\) respectively, are moving in opposite directions along the same straight line on a smooth horizontal plane. The particles collide directly and, as a result of the collision, the direction of motion of \(P\) is reversed and the direction of motion of \(Q\) is reversed. Immediately after the collision, the speed of \(P\) is \(v\) and the speed of \(Q\) is \(\frac { 3 v } { 2 }\). The coefficient of restitution between \(P\) and \(Q\) is \(\frac { 1 } { 5 }\).

1. Find
   1. the speed of \(P\) immediately before the collision,
   2. the speed of \(Q\) immediately before the collision. After the collision with \(P\), the particle \(Q\) moves on the plane and strikes at right angles a fixed smooth vertical wall and rebounds. The coefficient of restitution between \(Q\) and the wall is \(e\). Given that there is a further collision between the particles,
2. find the range of possible values of \(e\).