Find the 5-digit number whose digits are described as follows: The first digit is 2 less than 7. The third digit is 3 less than 5. The second digit is the product of the third digit and 3. The fourth

The first digit is 2 less than 7.

$$d_1 = 7 - 2 = 5$$

The third digit is 3 less than 5.

$$d_3 = 5 - 3 = 2$$

The second digit is the product of the third digit and 3.

$$d_2 = d_3 \times 3 = 2 \times 3 = 6$$

The fourth digit is the number that comes before the first digit.

$$d_4 = d_1 - 1 = 5 - 1 = 4$$

The last digit is the sum of the first and third digit.

$$d_5 = d_1 + d_3 = 5 + 2 = 7$$

The digits are $d_1=5$, $d_2=6$, $d_3=2$, $d_4=4$, $d_5=7$.
The number is 56247.

The 5-digit number is $\boxed{\text{56247}}$.