50. How many five-digit numbers are there that are divisible by 5 and do not have any repeated digits in their representation?
50. The number of numbers that end in 0 and do not have identical digits in their representation is $9 \cdot 8 \cdot 7 \cdot 6 \cdot 1$. The number of numbers that end in 5 and do not have identical digits in their representation is $8 \cdot 8 \cdot 7 \cdot 6 \cdot 1$. Therefore, the total number of numbers of interest to us is $9 \cdot 8 \cdot 7 \cdot 6+8 \cdot 8 \cdot 7 \cdot 6=5712$.