Integer all

n+11, n+22, n+33, n+44, n+55\dfrac{n+1}{1},\ \dfrac{n+2}{2},\ \dfrac{n+3}{3},\ \dfrac{n+4}{4},\ \dfrac{n+5}{5}

With n=0n=0, all of the above numbers are integers (they all equal 1). What is the next positive integer nn such that all of the above numbers are integers?

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