Calculation of autocorrelation - does calculation "loop"? With a delay $l$, autocorrelation is defined as: 
$$r_{xx}(l) = \sum_{n=-\infty}^{\infty}x(n)x(n-l) = \sum_{n=-\infty}^{\infty}x(n)x(n+l).$$

I want to calculate the autocorrelation of a signal 
$$x(n) = [1,2,3,4,5]$$
with delay $l=1$. The sum starts of as 
$$1*2+2*3+3*4+4*5..., $$
but what happens when I reach $n=5$? Do I start of in the beginning again, i.e is the autocorrelation
$$1*2+2*3+3*4+4*5 + 5*1$$
? Am I done there?
You didn't specify for which values of $n$ your signal is not zero, so I'll assume that happens from $0$ to $4$. You have a finite sequence $x(n)$ such that

$$x(n) = 0 \qquad \forall n\in\mathbb{Z}:n&lt;0 \ \mathrm{or} \ n&gt;4$$

This means that $x(5)$, $x(6)$, etc. are equal to $0$. The same happens for $x(-1)$, $x(-2)$, and so on. Thus, products involving these quantities will be zero as well.