Infinite Lumberjack

How do aliens chop wood? They don't. Instead, they breed (multiply) them using specific cloning codes.

If today's code produces F logs, and

$F=\lim _{ n\rightarrow \infty }{ (\log _{ n-1 }{ n } \cdot \log _{ n }{ (n+1) } \cdot ...\cdot \log _{ n^5-1 }{ n^5 }) }$ ,

then how many logs does this code produce?