6 Letters, 1 Number.

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How many ordered sets of integers \[(a,b,c,d,e,f)\] are there such that it satisfies the equations below? \[a^{5}=b\times c\times d\times e\] \[b^{5}= c\times d\times e\times f\] \[c^{5}=a\times d\times e\times f\] \[d^{5}=a\times b\times e\times f\] \[e^{5}=a\times b\times c\times f\] \[ f^{5}=a\times b\times c\times d\]

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