from typing import List
import unittest


def bitwise_or_with_trailing_zero(ints: List[int]) -> bool:
    """
    Determine if it's possible to select two or more elements from the list
    such that their bitwise OR has at least one trailing zero.

    Args:
    ints (List[int]): The input list of positive integers.

    Returns:
    bool: True if such a selection is possible, False otherwise.
    """
    n = len(ints)
    for i in range(n):
        for j in range(i + 1, n):
            if (ints[i] | ints[j]) % 2 == 0:
                return True
    return False


# Unit tests
class TestBitwiseOrWithTrailingZero(unittest.TestCase):
    def test_example_1(self):
        self.assertTrue(bitwise_or_with_trailing_zero([1, 2, 3, 4, 5]))

    def test_example_2(self):
        self.assertTrue(bitwise_or_with_trailing_zero([2, 3, 8, 16]))

    def test_example_3(self):
        self.assertFalse(bitwise_or_with_trailing_zero([1, 2, 5, 7, 9]))

    def test_no_trailing_zero(self):
        self.assertFalse(bitwise_or_with_trailing_zero([1, 3, 5, 7, 9]))

    def test_all_even(self):
        self.assertTrue(bitwise_or_with_trailing_zero([2, 4, 6, 8, 10]))


if __name__ == "__main__":
    unittest.main()