5. \(81^{5-x} = \frac{1}{3}\)

Решение: \(81 = 3^4\), следовательно, \(\left(3^4\right)^{5-x} = \frac{1}{3}\). \(3^{4(5-x)} = 3^{-1}\). \(4(5-x) = -1\). \(20-4x = -1\). \(4x = 21\). \(x = \frac{21}{4}\). Ответ: \(x = \frac{21}{4}\).