Final answer:
The least possible value of a^5-b^5 is 0.
Step-by-step explanation:
To find the least possible value of a5-b5, we can use the formula for the difference of fifth powers: a5-b5 = (a-b)(a4 + a3b + a2b2 + ab3 + b4). In this case, we know that a-b = 1, so we can substitute this value into the formula: (1)(a4 + a3b + a2b2 + ab3 + b4). Since we want to find the least possible value, we need to minimize the expression inside the parentheses.
One way to minimize the expression is to make the terms as small as possible. Since a and b are real numbers, the minimum value for a4 and b4 is 0, which means the terms a4 and b4 are 0. The other terms can be any real number, but we want to make them as small as possible as well.
One way to do this is to let a be as small as possible (which is 0) and let b be as large as possible (which is 1). Plugging in these values into the expression, we get: (1)(0 + 0 + 0 + 0 + 0) = 0. Therefore, the least possible value of a5-b5 is 0.