To solve this problem, we need to determine the first five terms of the sequence defined by the recursive rule:

1. $a_1 = 1$
2. $a_2 = 1$
3. $a_n = a_{n-2} + a_{n-1}$, for $n \geq 3$

Let's calculate the first five terms step by step:

1. $a_1 = 1$
2. $a_2 = 1$
3. $a_3 = a_1 + a_2 = 1 + 1 = 2$
4. $a_4 = a_2 + a_3 = 1 + 2 = 3$
5. $a_5 = a_3 + a_4 = 2 + 3 = 5$

The first five terms of the sequence are: $1, 1, 2, 3, 5$.

The correct answer is: $\{1, 1, 2, 3, 5\}$.

Do you want a detailed explanation about recursive sequences? Here are some questions to deepen your understanding:

1. How does a recursive formula differ from an explicit formula in sequences?
2. Why is it important to define initial conditions like $a_1$ and $a_2$ in a recursive sequence?
3. How can you verify if a sequence follows a given recursive rule?
4. What are some real-life applications of the Fibonacci sequence (which this example resembles)?
5. How can recursive sequences be represented graphically?

Tip: Always verify each step when calculating terms in recursive sequences to avoid propagation of errors!