2005 AMC 10B Problem 20

What is the average (mean) of all 5-digit numbers that can be formed by using each of the digits 1, 3, 5, 7, and 8 exactly once?

\mathrm{(A)} 48000 \qquad \mathrm{(B)} 49999.5 \qquad \mathrm{(C)} 53332.8 \qquad \mathrm{(D)} 55555 \qquad \mathrm{(E)} 56432.8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.