To solve this system of inequalities, we need to find the values of n that satisfy all three inequalities simultaneously.

1) 4n - 5 < 2n - 1
Simplify:
2n < 4
n < 2

2) 2n - 1 < 3n + 2
Simplify:
-n < 3
n > -3

3) 3n + 2 < n - 1
Simplify:
2n < -3
n < -1.5

Combining the results from all three inequalities, we find that n must be less than 2, greater than -3, and less than -1.5. However, the third inequality contradicts the first two, so there is no solution that satisfies all three inequalities simultaneously.