If David's new job pays $2400 per month and this amount is 5 times what he made at his previous job, we can find his previous monthly salary by dividing the new salary by 5:
\[ \text{Previous monthly salary} = \frac{2400}{5} = 480 \]
Now, to find David's yearly salary at his old job, we multiply his previous monthly salary by 12 (the number of months in a year):
\[ \text{Yearly salary at old job} = 480 \times 12 = 5760 \]
Thus, David's yearly salary at his old job was $5760.