Step-by-step explanation
In the question, we are given that Simon dilates ST by a scale factor of 5 through center C to produce line segment S'T'.
The dilation, in this case, implies that an enlargement of the pre-image ST has occured. This will then give an image S'T' which is 5 times the pre image.
![\begin{gathered} \therefore\text{ If S'T'=k}* ST \\ k\text{ would give 5, for the statement to hold} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/98cj0o58b8jifgslcs85h2do1rmn7fib6p.png)
Answer: 5