Given that:

\[ \begin{array}{lcr} ab=1 & bc=2 & cd= 3 \\ de=4 & ea=5 & b=? \\ \end{array}\]

with \(a,b,c,d\) and \(d\) positive numbers.Find \(b\)

If \(b=\dfrac{\sqrt{x!}}{y}\) where \(x<6\) is a prime,submit the answer as \(x+y\).

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