To transform the function $f(x) = x^3$ according to the given descriptions, we will apply the transformations step-by-step:

1. Shift 5 units to the left: This means we replace $x$ with $x + 5$. So the function becomes $f(x + 5) = (x + 5)^3$.

2. Shift 6 units down: To shift the graph down, subtract 6 from the function. So the equation becomes $(x + 5)^3 - 6$.

3. Reflect in the y-axis: Reflecting the function in the y-axis means replacing $x$ with $-x$. So the final function becomes: $g(x) = (-(x + 5))^3 - 6 = (-x - 5)^3 - 6$

Thus, the equation for the transformed function is: $g(x) = (-x - 5)^3 - 6$

Would you like a further breakdown of these transformations or additional clarifications?

Follow-up questions:

1. How do horizontal and vertical shifts affect the graph differently?
2. What would happen if the reflection was done over the x-axis instead?
3. How can you recognize the effects of transformations on other polynomial functions?
4. What other types of functions can be transformed similarly to this cubic function?
5. How would the graph change if we applied a vertical stretch or shrink?

Tip: When reflecting over the y-axis, the sign of $x$ is reversed, which flips the graph horizontally.