Let David's salary at his previous job be represented as \( x \).
According to the information given, David's new job pays $2400 per month, which is 5 times what he made at his previous job:
\[ 2400 = 5x \]
To find \( x \), we can solve the equation:
\[ x = \frac{2400}{5} = 480 \]
This means that David made $480 per month at his previous job.
To find his yearly salary at his old job, we multiply his monthly salary by 12 (the number of months in a year):
\[ 480 \times 12 = 5760 \]
Thus, David's yearly salary at his old job was $5760.