Answer
$12338352$
Work Step by Step
We know that the number of arrangements of $n$ objects in $r$ slots (where in a slot only $1$ of the $n$ elements can be put) is: $n^r$.
Thus the number of company names possible with $4$ letters: $26^4=456976.$
The number of company names possible with $5$ letters: $26^5=11881376.$
Thus the total is:$456976+11881376=12338352.$
