Nyquist-Shannon sampling theorem on non infinite signals
No need to think about "finite length". Even though continuous time signals are defined for infinite time interval, in practice we analyse it in a finite interval only. Your x(t) is defined in the interval [-5 5]. 



The frequency domain representation of such a signal will be an infinite bandwidth sinc function. 



Hence it is not possible define a particular sample rate as per nyquist theorem, to perfectly reconstruct it without losing any information. But you can sample it any definite sample rate, which then implicitly band limits the signal. This sampled signal after reconstruction through DAC and LPF, will not look as perfect as the original one as it would be band limited. It will have a finite transition time for rise and fall.