1. **State the problem:** We have a population with mean $\mu = 80$ and standard deviation $\sigma = 5$. We draw random samples of size $n = 100$. We want to find the mean of the sampling distribution of the sample mean. 2. **Formula and explanation:** The mean of the sampling distribution of the sample mean, often called the expected value of the sample mean, is equal to the population mean $\mu$. This is a fundamental property of the sampling distribution of the sample mean. 3. **Apply the formula:** Since $\mu = 80$, the mean of the sampling distribution of the sample mean is also: $$\bar{X} = \mu = 80$$ 4. **Interpretation:** This means that if we repeatedly take samples of size 100 from this population and calculate their means, the average of those sample means will be 80. **Final answer:** The mean of the sampling distribution of the sample mean is $80$.