The $5^{th}$ terms of the sequence defined by $\displaystyle t_{1}=2$,$\displaystyle t_{2}=3$ and $\displaystyle t_{n}=t_{n-1}+t_{n-2}$ for $\displaystyle n\geq 3$.

Using the Fibonacci recursive formula where each term is the sum of the two preceding terms, we calculate the terms sequentially starting from $t_1 = 2$ and $t_2 = 3$. The third term is $t_3 = 2 + 3 = 5$ and the fourth term is $t_4 = 3 + 5 = 8$. The fifth term is then calculated as $t_5 = 5 + 8 = 13$.

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