Step 1 :The sampling distribution of \(\bar{x}\) is approximately normal because the sample size is large enough.
Step 2 :The mean of the sampling distribution of \(\bar{x}\) is equal to the population mean, which is given as \(\mu=5\).
Step 3 :The standard deviation of the sampling distribution of \(\bar{x}\), also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size.
Step 4 :The population standard deviation is given as \(\sigma=\sqrt{5}\) and the sample size is 50.
Step 5 :Calculate the standard deviation of the sampling distribution of \(\bar{x}\) using the formula \(\sigma_{x} = \frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.
Step 6 :Substitute the given values into the formula: \(\sigma_{x} = \frac{\sqrt{5}}{\sqrt{50}}\).
Step 7 :Simplify to get \(\sigma_{x} = 0.316\).
Step 8 :Final Answer: The mean of the sampling distribution of \(\bar{x}\) is \(\mu_{x}=5\) and the standard deviation is \(\sigma_{x}=\boxed{0.316}\).