To find the total number of quizzes Chloe will have taken after 5 weeks of school, we start by determining the rate at which she takes quizzes per week.
Chloe took 32 quizzes over the course of 4 weeks. We calculate the number of quizzes she takes per week by dividing the total number of quizzes by the number of weeks:
\[ \text{Quizzes per week} = \frac{32 \text{ quizzes}}{4 \text{ weeks}} = 8 \text{ quizzes per week} \]
Now, to find out how many quizzes she will take after 5 weeks, we multiply the number of quizzes she takes per week by the number of weeks:
\[ \text{Total quizzes after 5 weeks} = 8 \text{ quizzes per week} \times 5 \text{ weeks} = 40 \text{ quizzes} \]
Therefore, after attending 5 weeks of school, Chloe will have taken a total of:
\[ \boxed{40} \text{ quizzes} \]
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