Code:
5^4 + 32^1 = 6^3 + 21^2 (625, 32, 216, 441)
5^4 + 34^2 = 12^3 + 53^1 (625, 1156, 1728, 53)
5^4 + 40^2 = 13^3 + 28^1 (625, 1600, 2197, 28)
5^4 + 42^1 = 7^3 + 18^2 (625, 42, 343, 324)
5^4 + 53^2 = 15^3 + 59^1 (625, 2809, 3375, 59)
5^4 + 56^1 = 8^3 + 13^2 (625, 56, 512, 169)
5^4 + 66^2 = 17^3 + 68^1 (625, 4356, 4913, 68)
5^4 + 75^1 = 6^3 + 22^2 (625, 75, 216, 484)
5^5 + 6^4 = 65^1 + 66^2 (3125, 1296, 65, 4356)
5^5 + 7^1 = 6^3 + 54^2 (3125, 7, 216, 2916)
5^5 + 7^4 = 50^1 + 74^2 (3125, 2401, 50, 5476)
5^5 + 8^3 = 37^1 + 60^2 (3125, 512, 37, 3600)
5^5 + 9^3 = 10^1 + 62^2 (3125, 729, 10, 3844)
5^5 + 10^3 = 8^4 + 29^1 (3125, 1000, 4096, 29)
5^5 + 16^2 = 6^1 + 15^3 (3125, 256, 6, 3375)
5^5 + 17^2 = 15^3 + 39^1 (3125, 289, 3375, 39)
5^5 + 18^2 = 15^3 + 74^1 (3125, 324, 3375, 74)
5^5 + 19^1 = 14^3 + 20^2 (3125, 19, 2744, 400)
5^5 + 20^1 = 6^4 + 43^2 (3125, 20, 1296, 1849)
5^5 + 27^1 = 7^3 + 53^2 (3125, 27, 343, 2809)
5^5 + 32^2 = 8^4 + 53^1 (3125, 1024, 4096, 53)
5^5 + 32^2 = 16^3 + 53^1 (3125, 1024, 4096, 53)
5^5 + 33^1 = 13^3 + 31^2 (3125, 33, 2197, 961)
5^5 + 43^2 = 17^3 + 61^1 (3125, 1849, 4913, 61)
5^5 + 47^1 = 12^3 + 38^2 (3125, 47, 1728, 1444)
5^5 + 55^1 = 11^3 + 43^2 (3125, 55, 1331, 1849)
5^5 + 59^2 = 9^4 + 45^1 (3125, 3481, 6561, 45)
5^5 + 60^1 = 7^4 + 28^2 (3125, 60, 2401, 784)
5^5 + 60^1 = 14^3 + 21^2 (3125, 60, 2744, 441)
5^6 + 8^4 = 27^3 + 38^1 (15625, 4096, 19683, 38)
5^6 + 16^1 = 10^3 + 11^4 (15625, 16, 1000, 14641)
5^6 + 20^4 = 9^1 + 56^3 (15625, 160000, 9, 175616)
5^6 + 35^2 = 7^5 + 43^1 (15625, 1225, 16807, 43)
5^6 + 45^2 = 26^3 + 74^1 (15625, 2025, 17576, 74)