What is the number of digits in $(33{)}^3$?

Let's calculate the exact value of $(33{)}^3$:
$$(33{)}^3=33\times 33\times 33$$

First, find $33\times 33$:

$$33^2=1089$$

Now, multiply $1089$ by $33$:

$$1089\times 33=1089\times (30+3)$$

$$1089\times 30=32670$$

$$1089\times 3=3267$$

$$\text{Total}=32670+3267=35937$$

The value of $(33{)}^3$ is $35937$.
Counting the digits in $35937$, we find there are exactly $5$ digits.