G3 up by a perfect fifth is D4, D4 up by P5 is A5!! A5 up by P5 is E5. It's all good except that the A string is tuned to A4, which is 440Hz. Why should not be tuned to A5?! Why is the tuning G3, D4, A4 and E5 instead of G3, D4, A5 and E5?
As user25119 wrote, the octave numbers change when you go from B to C. So that means the D and the A highlighted below should have the same octave number.
- The octave starting with middle C has octave number 4, so the octave from middle C up to the B above middle C is C4 D4 E4 F4 G4 A4 B4.
- The octave above that, of course, is octave number 5, which is why the high E on the violin is E5.
D4 up by a perfect fifth is A4. The octave number in the scientific note naming system only advances when crossing the B/C boundary, so the C major scale notes available on the violin (notes on open strings marked) are
G3(open) A3 B3 C4 D4(open) E4 F4 G4 A4(open) B4 C5 D5 E5(open) F5 ...