1. The problem is to find the first term in a Fibonacci-type sequence where the second term is 5 and the fifth term is 23. 2. Recall the Fibonacci-type sequence rule: each term is the sum of the two preceding terms. 3. Let the first term be $x$. Then the sequence terms are: - First term: $x$ - Second term: 5 - Third term: $x + 5$ - Fourth term: $5 + (x + 5) = x + 10$ - Fifth term: $(x + 5) + (x + 10) = 2x + 15$ 4. We know the fifth term is 23, so set up the equation: $$2x + 15 = 23$$ 5. Solve for $x$: $$2x = 23 - 15$$ $$2x = 8$$ $$x = 4$$ 6. Therefore, the first term is 4. 7. The sequence starts as: 4, 5, 9, 14, 23, ... This satisfies the Fibonacci-type rule and the given terms.