What is the smallest number that leaves remainders of 1, 2, 3, 4, and 5 when divided by 6, 7, 8, 9, and 10 respectively, and is also exactly divisible by 19?

Explanation

The number must satisfy the conditions of leaving specific remainders when divided by 6, 7, 8, 9, and 10, and be divisible by 19 without remainder. Among the given choices, only 5035 meets all these criteria.