Number Choosing Contest.

78, 79, 80, 81, 82

78: breaks YZ & 1, 2, 3, 4 and 5.
79: breaks YZ & 1, 3 and 4.
80: breaks YZ & 2, 3, 4 and 5.
81: breaks YZ & 1, 2, 3 and 5.
82: breaks YZ & 1, 3, 4 and 5.