We are given the complex numbers $z_1 = 1 + i$ and $z_2 = 5$ (after simplification). We need to find a complex number $w = a + bi$ such that $w z_1 = z_2$.

The equation $w z_1 = z_2$ simplifies to $w = \frac{z_2}{z_1}$, which leads to the solution $a = \frac{5}{2}$ and $b = -\frac{5}{2}$.

Thus, the complex number $w$ is:

$w = \frac{5}{2} - \frac{5}{2}i$

If you want more details or have any questions, feel free to ask!

Here are 5 related questions:

1. How do you divide complex numbers?
2. What is the geometric interpretation of multiplying complex numbers?
3. How can you express the conjugate of a complex number?
4. What are the properties of complex number multiplication?
5. How do you find the modulus of a complex number?

Tip: When solving for a complex number, it can help to express both sides in the form $a + bi$ to simplify the comparison of real and imaginary parts.