A capacitor with a capacitance of 500 is connected to a battery via...

The time constant of the $RC$ circuit is given by $\tau = RC$.

Substituting the given values:

$\tau = (10 \times 10^3) \times (500 \times 10^{-6}) = 5 \text{ s}$

The charge on the capacitor as a function of time is $q(t) = q_0(1 - e^{-t/\tau})$, where $q_0$ is the maximum steady-state charge.

The charge stored during the initial $5 \text{ s}$ ($t = \tau$) is:

$q_1 = q(5) - q(0) = q_0(1 - e^{-1}) \approx 0.632 q_0$

The maximum possible charge that can be stored in all subsequent time ($t = 5 \text{ s}$ to $t \to \infty$) is:

$q_{\text{remaining}} = q(\infty) - q(5) = q_0 - 0.632 q_0 = 0.368 q_0$

Since $0.632 q_0 > 0.368 q_0$, the charge stored in the initial $5 \text{ s}$ is strictly greater than the total charge stored in any subsequent time interval, regardless of its duration.

Therefore, the charge stored in the initial $5 \text{ s}$ is larger than the charge stored in the subsequent $5 \text{ s}$, $50 \text{ s}$, $500 \text{ s}$, and $5000 \text{ s}$.