Answer: Key sketch points include \((-90^\circ,2)\), \((-45^\circ,-8)\), \((0,2)\), \((45^\circ,-8)\), \((90^\circ,2)\); amplitude \(5\); period \(90^\circ\).

For \(y=5\cos4x-3\), calculate key values in the given interval.

At \(x=0^\circ\),

\(y=5\cos0^\circ-3=2.\)

At \(x=\pm45^\circ\),

\(4x=\pm180^\circ,\qquad y=5(-1)-3=-8.\)

At \(x=\pm90^\circ\),

\(4x=\pm360^\circ,\qquad y=5(1)-3=2.\)

The graph also crosses its midline \(y=-3\) at \(x=\pm22.5^\circ\) and \(x=\pm67.5^\circ\).

The amplitude is the magnitude of the coefficient of the cosine term:

\(\boxed{5}.\)

The period is

\(\frac{360^\circ}{4}=\boxed{90^\circ}.\)