To find g(f(4)), work from the inside out.
f(4) is 4^2+3, or 16+3, or 19. Now, we must find g(19).
This is 19+5/19. This is already a mixed number, though if you want an improper fraction solution, we have:
361/19+5/19
Which simplifies to:
366/19
Therefore, 366/19 is the answer.