Long Sequences...

If \[\frac {\binom{n}{r}+ 4 \binom{n}{r+1} + 6 \binom{n}{r+2} + 4 \binom{n}{r+3} + \binom{n}{r+4}}{\binom{n}{r} + 3 \binom{n}{r+1} + 3 \binom{n}{r+2} +\binom{n}{r+3}} = \frac{n + k}{r + k}\] then the value of k is

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