Solved – Autocorrelation vs correlation calculation

I have set $x = {1,2,3,4,5}$ and set $y = {2,3,4,5,6}$. Lets say the correlation of $x$ and $y$ is $0.7$. If I then have set $z = {1,2,3,4,5,2,3,4,5,6}$, and I do autocorrelation using lag $=$ $5$, should I not get the same $0.7$? I have been doing this but I keep getting different results. I'm wondering if I'm doing something wrong, or maybe it is that they should have different results.

denominators are different in the correlation formula and the autocorrelation formula. (moved to answer at moderator's request)

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