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log₅2*(log₅125/log₅64)*(log₅4/log₅√5)*(log₅5/log₅8) =
log₅2*(log₅(5)³/log₅(2)⁶)*(log₅(2)²/log₅(5)^½)*(1/log₅(2)³) =
log₅2*(3log₅5/6log₅2)*(2log₅2/½log₅5)*(1/3log₅2) =
(3/6)*(2log₅2/½)*(1/3log₅2) = ½*4*⅓ = ⅔