Answer
The maximum number of companies that can be listed on NASDAQ is 12,338,352.
Work Step by Step
With 4 letters: $26\times26\times26\times26=456,976$ possibilities.
With 5 letters: $26\times26\times26\times26\times26=11,881,376$ possibilities.
Total: $456,976+11,881,376=12,338,352$ possibilities.