Any of 9 digits at the most-left position,  giving 9 possible options;
       (any of ten digits, except of 0);

Any of remaining 10-1 = 9 digits at the next position,  giving 9 possible options;

Any of remaining  9-1 = 8 digits at the next position,  giving 8 possible options;

Any of remaining  8-1 = 7 digits at the next position,  giving 7 possible options;

Any of remaining  7-1 = 6 digits at the next position,  giving 6 possible options.


Thus in total, there are  9*9*8*7*6 = 27216 different 5-digit numbers as described.