Answer: \(a=-1\), \(b=5\), \(c=3\).

The graph meets the \(y\)-axis at \((0,-1)\). Since \(\sin0^\circ=0\),

\(f(0)=a=-1.\)

The amplitude is \(5\), and \(b\gt 0\), so

\(b=5.\)

The period of \(a+b\sin cx\) is \(\dfrac{360^\circ}{c}\). Hence

\(\frac{360^\circ}{c}=120^\circ,\qquad c=3.\)

The sketch is a sine curve with midline \(y=-1\), maximum value \(4\), minimum value \(-6\), and period \(120^\circ\). It starts at \((0,-1)\), reaches a maximum at \(30^\circ\), returns to the midline at \(60^\circ\), reaches a minimum at \(90^\circ\), and repeats this cycle every \(120^\circ\).