Sketch 5cos(t); energy or power

$x(t) = 5\cos t$ has amplitude 5 and $\omega_0 = 1$ rad/s, so period $T_0 = 2\pi/1 = 2\pi \approx 6.28$ s. Peaks of $+5$ at $t = 0, \pm2\pi, \ldots$; zeros at $t = \pm\pi/2, \pm3\pi/2$; minimum $-5$ at $t = \pm\pi$.

 x(t)
  5 +.                   .
    | '.               .'
  0 +---'.---------.'-------> t
    |  pi/2 '.   .' 3pi/2
 -5 +         '-'
    0         pi        2pi

(The waveform repeats every $2\pi$ s for all $t$, also for negative $t$, since cosine is even.)

Energy or power

Energy:

$$E = \int_{-\infty}^{\infty}25\cos^2 t\,dt = \infty$$

Power (periodic signal, average over one period):

$$\begin{aligned} P &= \frac{1}{2\pi}\int_0^{2\pi}25\cos^2 t\,dt = \frac{25}{2\pi}\int_0^{2\pi}\frac{1+\cos 2t}{2}\,dt \\ &= \frac{25}{2\pi}\cdot\pi = \frac{25}{2} = 12.5 \end{aligned}$$

Answer: $x(t) = 5\cos t$ is a power signal with $P = 12.5$ W (normalised to 1 Ω) and $E = \infty$.