Add PlotRange -> All
or reduce the x
range
Plot[Piecewise[
{{5.66048 E^(0.76` x), x < -5},
{0.398447 Cos[0.25 x], -5 <= x <= 5},
{5.66048 E^(-0.76` x), x > 5}}, 0],
{x, -10, 10}]

LogPlot[Piecewise[
{{5.66048 E^(0.76` x), x < -5},
{0.398447 Cos[0.25 x], -5 <= x <= 5},
{5.66048 E^(-0.76` x), x > 5}}, 0],
{x, -10, 10}]
