GATE DA 2024 Q57: Exponential rate when 5E(X) equals Var(X)

Let $X$ be a random variable exponentially distributed with parameter $\lambda > 0$. The probability density function of $X$ is given by:

$$f_X(x) = \begin{cases} \lambda e^{-\lambda x}, & x \ge 0 \\ 0, & \text{otherwise} \end{cases}$$

If $5E(X) = Var(X)$, where $E(X)$ and $Var(X)$ indicate the expectation and variance of $X$, respectively, the value of $\lambda$ is ______ (rounded off to one decimal place).