5. Consider the linear model with intercept:
$y_t = \alpha + \beta x_t + u_t$
If the $A = \sum_{i=1}^{n} (x_i - \bar{x})^2$ is positive definite and $E(u_i \mid x_i) = 0, \forall t = 1, 2, \dots, T$, which statement is true under sample size $T \to \infty$.
(A) \( \hat{\beta} \) is consistent, but we cannot judge whether \( \hat{\beta} \) is efficiency
(B) \( \hat{\beta} \) is unbiased and efficiency
(C) \( \hat{\beta} \) is consistent and efficiency
(D) \( \hat{\beta} \) is, but we cannot judge whether \( \hat{\beta} \) is efficiency
(E) \( \hat{\beta} \) is unbiased and consistent.