Consider five unique numbers represented by the letters A through E, each ranging from 1 to 5. Determine the specific value for each of these letters given the following conditions:
The sum of A and D equals C (A + D = C),
E is not equal to 5 (E ≠ 5),
The sum of D and E equals the sum of B and C (D + E = B + C),
C is equal to D plus 1 (D + 1 = C).
The goal is to find the distinct numbers from 1 to 5 that A, B, C, D, and E represent, satisfying all the given conditions.