If 100 five-cent coins were stacked on top of each other in a column, the column would be approximately $6\dfrac{5}{8}$ inches tall. At this rate, which of the following is closest to the number of five-cent coins it would take to make an $15$-inch-tall column?

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We can set up a simple proportion:

$$\frac{100 \text{ coins}}{6 \frac{5}{8} \text{ inches}}= \frac{x \text{ coins}}{15 \text{ inches}}$$ $$6 \frac{5}{8} \cdot x = 15 \cdot 100$$ $$x \approx \boxed{226} \text{ coins}$$