We note the following:
I. New clients are received randomly at a rate of 2 per unit time (month)
II. Each event is independent

These observations confirm the Poisson distribution.

Since the question asks us to find a yearly probability, we must convert the monthly Poisson rate to an equivalent yearly rate.

Poi(1) monthly distribution is equivalent to Poi(12) yearly.

Now, if X stands for the number of clients received,

$$P(X = x) = \frac{[\exp(-\lambda)\lambda^x]}{x!}$$ $$P(X = 5) = \frac{[\exp(-12)12^5]}{5!} = 0.01274$$