$$[(\frac{-8}{13})^{-1}+(\frac{14}{5})^{-1}]\div(\frac{24}{5})^{-1}$$
$-\frac{213}{35}\approx -6.085714286$
$$\frac{\left(-\frac{8}{13}\right)^{-1}+\left(\frac{14}{5}\right)^{-1}}{\left(\frac{24}{5}\right)^{-1}}$$
$$\frac{-\frac{13}{8}+\left(\frac{14}{5}\right)^{-1}}{\left(\frac{24}{5}\right)^{-1}}$$
$$\frac{-\frac{13}{8}+\frac{5}{14}}{\left(\frac{24}{5}\right)^{-1}}$$
$$\frac{-\frac{71}{56}}{\left(\frac{24}{5}\right)^{-1}}$$
$$\frac{-\frac{71}{56}}{\frac{5}{24}}$$
$$-\frac{71}{56}\times \frac{24}{5}$$
$$-\frac{213}{35}$$
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$-\frac{213}{35} = -6\frac{3}{35} = -6.085714285714285$
