If the resultant of a two perpendicular identical vectors is 5 units and one of them makes a sixty degrees angle what is its magnitude?

You wrote "if the resultant of two perpendicular identical vectors ..." OK, so you have two vectors at right angles to each other which you are adding together, and by "identical" I assume you mean both vectors have the same magnitude. But then you say "one of them makes a 60 degree angle" - 60 degrees to what? You said they were perpendicular to each other, so this makes no sense - please clarify.