Answer: \(a=4\), \(b=3\), \(c=-5\).

For a trigonometric graph, identify the amplitude, midline and period first, then use these to locate the key points of the sketch.

From the graph, the maximum value is \(-1\) and the minimum value is \(-9\).

The midline is therefore

\(\frac{-1+(-9)}2=-5\),

so \(c=-5\).

The amplitude is

\(\frac{-1-(-9)}2=4\),

so \(a=4\).

For \(y=4\cos\left(\frac{x}{b}\right)-5\), the graph has a maximum at \(x=0\) and the next minimum at \(x=540^\circ\). A maximum to a minimum is half a period, so the period is \(1080^\circ\).

The period of \(\cos\left(\frac{x}{b}\right)\) is \(360b^\circ\), so

\(360b=1080\).

Hence \(b=3\).

Therefore \(a=4\), \(b=3\), and \(c=-5\).