Esquecinaldo has a terrible memory for remembering numbers, but excellent for remembering sequences of operations. Therefore, to remember his 5-digit bank code, he can remember that none of the digits are zero, the first two digits form a power of 5, the last two digits form a power of 2, the middle digit is a multiple of 3, and the sum of all the digits is an odd number. Now he no longer needs to memorize the number because he knows it is the largest number that satisfies these conditions and has no repeated digits. What is this code?