These are combinations with repeats allowed. So, we have:
[5 + 3 - 1]C3 =7C3 = 35. Here are all your combinations:
{A, A, A} | {A, A, B} | {A, A, C} | {A, A, D} | {A, A, E} | {A, B, B} | {A, B, C} | {A, B, D} | {A, B, E} | {A, C, C} | {A, C, D} | {A, C, E} | {A, D, D} | {A, D, E} | {A, E, E} | {B, B, B} | {B, B, C} | {B, B, D} | {B, B, E} | {B, C, C} | {B, C, D} | {B, C, E} | {B, D, D} | {B, D, E} | {B, E, E} | {C, C, C} | {C, C, D} | {C, C, E} | {C, D, D} | {C, D, E} | {C, E, E} | {D, D, D} | {D, D, E} | {D, E, E} | {E, E, E} (total: 35)