A

Step 1: Analyze the structure of the capacitor
The capacitor consists of a flat bottom plate with area $5a \cdot w$ (where $w$ is the width of the plates) and a stair-like top plate. The total height of the stair-like structure is $d$ and it has alternating heights and widths as shown.
Step 2: Calculate the effective area
The top plate can be thought to consist of several steps. Each step has a width of $a$ and a height of $d$. The effective area of the top plate ($A_{top}$) can be calculated as:
$$ A_{top} = n \cdot a \cdot d$$, where $n$ is the total number of steps.
Since the total width of the bottom plate is $5a$, the number of steps $(n)$ can be determined by examining the pattern of the stairs. There are effectively $5$ steps visible, each contributing to the top plate area.
Step 3: Determine the capacitance formula
The capacitance ($C$) of a capacitor is given by the formula:
$$ C = \frac{\varepsilon A}{d_{eff}}$$
where $A$ is the overlapping area between the plates and $d_{eff}$ is the distance between the plates. Since each segment has a height of $d$, the effective separation remains as $d$.
Step 4: Calculate total capacitance
Now substituting $A_{top}$ and the distance between plates into the capacitance formula gives us:
$$ C = \frac{\varepsilon (5ad)}{d} = 5\varepsilon a$$
Thus, each combination of areas adds up, giving the final answer as:
Therefore, the capacitance of the assembly is:
$$ C = 5\varepsilon a $$.