Question 549512
Here's why:

Suppose you had this long list of them to add:    

 13579         
 13597         
 13759                  
 .....
 .....
 97351         
 97513         
 97531         
------

There would be 5! or 120 numbers to add.  Each vertical column of digits
contains an equal number of 1's, 3's, 5's, 7's and 9's.  So since 120÷5
is 24, the sum of each column is 24×(1+3+5+7+9) = 600, The first column
represents 10000's, the 2nd column represents 1000's, etc.  Therefore the
sum is:

600×10000 + 600×1000 + 600×100 + 600×10 + 600 =

600×(10000 + 1000 + 100 + 10 + 1) =

600×(11111) = 6666600 

Edwin</pre>