Помогите пожалуйста!!!! решите уравнение: |y+3| - |y-2|=5

Решите задачу:

$|y+3| - |y-2|=5, \\ y+3=0, y=-3, \\ y-2=0, y=2, \\ \left \{ {{y<-3,} \atop {-(y+3)+(y-2)=5;}} \right. \left \{ {{y<-3,} \atop {-y-3+y-2=5;}} \right. \left \{ {{y<-3,} \atop {0\cdot y=10;}} \right. \left \{ {{y<-3,} \atop {y\in\varnothing;}} \right. \\ y\in\varnothing; \\ \\ \left \{ {{-3 \leq y< 2,} \atop {(y+3)+(y-2)=5;}} \right. \left \{ {{-3 \leq y< 2,} \atop {y+3+y-2=5;}} \right. \left \{ {{-3 \leq y< 2,} \atop {2y=4;}} \right. \left \{ {{-3 \leq y< 2,} \atop {y=2;}} \right.$
$y\in\varnothing; \\ \\ \left \{ {{y \geq 2,} \atop {(y+3)-(y-2)=5;}} \right. \left \{ {{y \geq 2,} \atop {y+3-y+2=5;}} \right. \left \{ {{y \geq 2,} \atop {0\cdot y=0;}} \right. \left \{ {{y \geq 2,} \atop {y\in R;}} \right. \\ y \geq 2, \\ y\in[2;+\infty).$