Generate Variables in C#

What you need is called an Array. It is the simplest collection of variables you can create:

int[] IDs = new int[5];
for (int i = 0; i < IDs.Length; i++)
   {
   Console.Write("ID {0} : ", i + 1);
   IDs[i] = Convert.ToInt32(Console.ReadLine());
   } 

Please see my comment to the question, which is probably based on some misconception. Probably you will be able to understand it from this comment. Consider this:

int length = //...
int[] ids = new int[length];

for (int index = 0; index < length; ++index) {
    Console.Write(" ID {0}: ", index + 1);
    ids[index] = int.Parse(Console.ReadLine());
}

Array is just one way of having the objects (of the integer type, in this case) which are created, can be accessed, manipulated, but have no individual names, such as variables. Objects do not have to have individual names, and, in many cases, cannot have them. Other cases include collections, arbitrary object graphs linked by managed pointers (references), with linked lists or trees being simple example of such graphs.

—SA

Instead of using an array, you can also use a List[^]:

List<int> IDs = new List<int>();
for(int i = 0; i < 5; i++)
{
    Console.Write(" ID {0} : ",i+1);
    IDs.Add(Convert.ToInt32(Console.ReadLine()));
}

Now, you can get the first value of the List with IDs[0], you can get the second value of the List with IDs[1], ...