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