Yes, there you've got an object array which happens to contain strings,
rather than a string array. You can't cast an object array to a string
array, despite all the contained objects being strings. (Just think
what would happen if you set myobjarray[i] = new object() afterwards.)

You can use Array.Copy though:

using System;

class Test
{
   static void Main()
   {
       object[] myobjarray = new object[5];
       for(int i=0;i<5;i++)
       {
           myobjarray[i] = (object)i.ToString();
       }

       string[] mystrarray = new string[myobjarray.Length];
       Array.Copy(myobjarray, mystrarray, myobjarray.Length);
       
       foreach (string x in mystrarray)
       {
           Console.WriteLine (x);
       }
   }
}