Stop doing this:

using namespace std;

Its a really bad habit that is hard to break later and can cause some real problems. The reason the standard namespace is called std and not standard is so that prefix them members with std:: is not that much of a burden.

Usually user defined types start with an initial uppercase letter.
While anything that can be an object starts with a lower case letter. Its a pretty standard convention for C++.

const int ListSize = 5;
int ValuesProcessed = 0;
float ValueSum = 0;

Prefer to use "\n" in preference to std::endl. The difference is that "\n" does not force a flush. Which can be very costly. Let the system handle that for you and flush at optimal times (it does that automatically). Even with std::cin/std::cout were you think you need to flush before asking for input; you don't if you read from std::cin then std::cout is automatically flushed to make sure that the user sees the question they are trying to answer.

cout << "Please enter " << ListSize << " numbers" << endl;

Its would be nice to give some user feedback here.

    float Value;
    cin >> Value;

Also you don't check and fix bad input. What happens if I accedently typed "fred" What do you think would happen?

Don't bother to return 0 from main(). By not returning a value you are indicating that there are no possible error conditions. Note: main() is special in that it is the only function that the compiler will implicitly plant a return 0; for you if you miss it out.

Stop doing this:

using namespace std;

Its a really bad habit that is hard to break later and can cause some real problems. The reason the standard namespace is called std and not standard is so that prefix them members with std:: is not that much of a burden.

Usually user defined types start with an initial uppercase letter.
While anything that can be an object starts with a lower case letter. Its a pretty standard convention for C++.

const int ListSize = 5;
int ValuesProcessed = 0;
float ValueSum = 0;

Prefer to use "\n" in preference to std::endl. The difference is that "\n" does not force a flush. Which can be very costly. Let the system handle that for you and flush at optimal times (it does that automatically). Even with std::cin/std::cout were you think you need to flush before asking for input; you don't if you read from std::cin then std::cout is automatically flushed to make sure that the user sees the question they are trying to answer.

cout << "Please enter " << ListSize << " numbers" << endl;

Its would be nice to give some user feedback here.

    float Value;
    cin >> Value;

Also you don't check and fix bad input. What happens if I accedently typed "fred" What do you think would happen?

Don't bother to return 0 from main(). By not returning a value you are indicating that there are no possible error conditions. Note: main() is special in that it is the only function that the compiler will implicitly plant a return 0; for you if you miss it out.