The answer is:

We solve the inequality as 5cos((pi/12)(x-3))-2 < 0:
Calculator screen image. Calculator screen image. Calculator screen image.
The period will be 2π(12/π) = 24, so we set the domain
for the WINDOW accordingly.
The range will be -2-5 = -7 to -2+5 = 3, so we set the
range for the WINDOW to at least -7 to 3.
Calculator screen image. Calculator screen image.
The solution set is approximately (7.43, 22.57).

Calculator screen image.
Using TRACE, the graph gives negative y-values
(graph is below the x-axis) between the intercepts.

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