Using the Circle Of Fifth’s, you can actually figure out the order of sharps by simply remembering the acronym “Father Charles Goes Down And Ends Battle”.
The placements of the letters in the acronym are the #’s in the letters of the circle of fifth’s. For example, in G# there is 1 #, F#, because that’s the placement on the acronym and circle. Another example is for E#, they have 4 #’s which will be F#, C#, G# and D# because they take the rest of the #’s and add another.
These work out key signature’s.