The exercise involves calculating the value of $x$ using the diagram where several parallel lines and triangle similarity properties can be applied. Here's a breakdown of the problem:

• The lines $AB \parallel CD \parallel CE$, according to the instructions.
• We are given:
  • $AB = 5$ cm,
  • $CD = 3$ cm,
  • and we need to calculate $x = DE$.

Applying Thales' Theorem

Thales' Theorem (in this context) relates the proportional lengths of segments created by parallel lines on transversals.

Using the similarity of triangles $AMB$ and $CMD$, we can set up a proportion:

$\frac{AB}{CD} = \frac{AD}{DE}.$

Now, let's substitute the known values: $\frac{5}{3} = \frac{AD}{x}.$

To solve for $x$, we need the value of $AD$. From the diagram, $AD = AB + BD$. However, $BD$ is not directly given. Would you like to clarify the value of $AD$ or provide more information from the problem?

Let me know if you'd like further details or guidance! Here's how you can proceed:

1. Can you confirm if the full length of $AD$ is provided elsewhere?
2. Do you have more information about any specific triangle properties?
3. Are there any other segment lengths noted in the problem?
4. Would you like an explanation of how Thales' Theorem applies?
5. Would you like to explore other methods if more data were available?

Tip: Always ensure to check all geometric properties (such as angles or parallel lines) when applying theorems like Thales' or the triangle similarity rules.