What is the greatest possible integer among five integers formed from ten digits, between 10 and 99?

To determine the greatest possible integer among five integers formed from ten digits ranging from 10 to 99, we need to consider the largest two-digit numbers possible. The two-digit integers can be formed using the digits 0-9, where the first digit cannot be 0 since it would not represent a two-digit number.

Among the choices given, the number 99 is the largest two-digit integer possible. It uses both digits available (9 and 9), which are among the digits from 0 to 9 allowed for forming these integers.

Other numbers such as 96, 97, and 98, while close, are all lesser than 99. It's not just about being in the range between 10 and 99; it's about finding the maximum achievable value using the available digits where repetition of digits is allowed.

Thus, 99 stands out as the greatest integer that can be formed under the specified conditions.