5. Among the numbers between 4000 and 7000, there are $\qquad$ numbers that are even and have four distinct digits.

Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
5. 728 First, count the numbers that meet the requirements and have 4 or 6 as the thousands digit. In this case, there are 2 choices for the thousands digit, so there are 4 choices for the units digit (selected from $0,2,4,6,8$), 8 choices for the hundreds digit, and 7 choices for the tens digit. Therefore, there are $2 \times 4 \times 8 \times$ $7=448$ such integers. Similarly, if the thousands digit is 5, there are $1 \times 5 \times 8 \times 7=280$ even numbers that meet the requirements. Therefore, there are a total of $448+280=728$ numbers.