Suppose that in a memory experiment the rate of memorizing is given by $M^{\prime}(t)=-0.009 t^{2}+0.2 t$, where $M^{\prime}(t)$ is the memory rate, in words per minute. How many words are memorized during minutes $5-10$ ?

Step 1 ：Given that the rate of memorizing is given by the function \(M^{\prime}(t)=-0.009 t^{2}+0.2 t\), where \(M^{\prime}(t)\) is the memory rate in words per minute.

Step 2 ：To find the total number of words memorized during a certain time interval, we need to integrate the rate function over that interval.

Step 3 ：In this case, we need to integrate from \(t=5\) to \(t=10\).

Step 4 ：Performing the integration, we find that the total number of words memorized from minute 5 to minute 10 is 4.875.

Step 5 ：Final Answer: The total number of words memorized during minutes 5-10 is \(\boxed{4.875}\).