1. **State the problem:** We have a Fibonacci-type sequence where each term is the sum of the two previous terms. The sequence is: $a_1$, 5, $a_3$, $a_4$, 23, ... We need to find the first term $a_1$. 2. **Recall the rule:** For Fibonacci-type sequences, each term after the first two is given by: $$a_n = a_{n-1} + a_{n-2}$$ 3. **Write equations for the known terms:** - $a_3 = a_2 + a_1 = 5 + a_1$ - $a_4 = a_3 + a_2 = (5 + a_1) + 5 = a_1 + 10$ - $a_5 = a_4 + a_3 = (a_1 + 10) + (5 + a_1) = 2a_1 + 15$ 4. **Use the given value for $a_5$:** $$2a_1 + 15 = 23$$ 5. **Solve for $a_1$:** $$2a_1 = 23 - 15$$ $$2a_1 = 8$$ $$a_1 = \frac{8}{2}$$ $$a_1 = 4$$ 6. **Conclusion:** The first term of the sequence is $4$. **Final answer:** $\boxed{4}$