To find the depth of the container, we can use the volume formula for a cube:

$V = s^3$

where $V$ is the volume of the cube and $s$ is the length of an edge (depth, in this case).

Given the volume $V = 125 \, \text{cm}^3$, we can solve for $s$ by taking the cube root of both sides:

$s = \sqrt[3]{125}$

$s = 5 \, \text{cm}$

So, the depth of the container is 5 cm.

Let me know if you'd like further clarification!

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Here are some related questions:

1. How would the volume change if the edge length was doubled?
2. What would the volume be if the cube's edge length was halved?
3. How can we find the surface area of the cube?
4. How do you calculate the volume of a rectangular prism, and how does it differ from a cube?
5. How do you convert the volume of a cube from cm³ to liters?

Tip: To quickly find the cube root of a number, use a scientific calculator or the nth root function on a graphing calculator.