For a first order reaction A → Products, initial concentration of A...

The integrated rate equation for a first order reaction is given by

$k = \dfrac{2 . 303}{t}log\dfrac{a}{a - x}$

Where

$k = Rateconstanta = initialconcentrationofthereactantsa - x = concentrationofreactantsleftaftertime, t .$

$k = \dfrac{2 . 303}{5}log\dfrac{0 . 1}{0 . 001} = \dfrac{4 . 606}{5} = 0 . 9212\min^{- 1}$

Hence, the rate constant of the given reaction is $0 . 9212\min^{- 1}$