Given
[tex]-5x-13y-66=0[/tex]Transform it into its slope-intercept form, as shown below
[tex]\begin{gathered} \Rightarrow y=-\frac{5}{13}x-\frac{66}{13} \\ \end{gathered}[/tex]Then, the slope of the line is -5/13.
On the other hand, the inclination angle of a line is given by the formula below
[tex]\begin{gathered} m=tan\theta \\ \Rightarrow\theta=\tan^{-1}(m) \\ \theta\rightarrow\text{ inclination angle} \\ m\rightarrow\text{ slope} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} \Rightarrow\theta=\tan^{-1}(-\frac{5}{13}) \\ \Rightarrow\theta=-0.3671738...\text{ radians} \\ or \\ \theta=-21.04\degree \end{gathered}[/tex]