[c#] C# declare empty string array

Your syntax is invalid.

string[] arr = new string[5];

That will create arr, a referenced array of strings, where all elements of this array are null. (Since strings are reference types)

This array contains the elements from arr[0] to arr[4]. The new operator is used to create the array and initialize the array elements to their default values. In this example, all the array elements are initialized to null.

Single-Dimensional Arrays (C# Programming Guide)