Infinitely many mathematicians walk into a bar. The first says "I'll have a beer". The next ones say "I'll have half of the previous guy". The bartender pours out 2 beers and says "Know your limits".

What is the value of \[\lim_{x \to 0} \frac{5}{x}\left(\frac{1}{x+1}-\frac{1}{5x+1}\right)?\]

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