Not true. If you are talented you can go straight to Grade 5 as your 1st exam.
But your teacher would prefer you to take one grade per year so you can pay her big bucks.

It means you do not have to sit for Grades 1 - 4 but straight away take Grade 5 as your 1st exam. That was my experience with the external grade exams of Trinity College. I do not know which examining body you are aiming for or if the rules have changed.

I will try to explain in a simple manner without further confusing you.
First you learn to stand up. Then you learn to walk. Then you learn to run. And then you advance to jumping and so on and so forth.
Let's say learning to stand is Grade 1. Learning to walk is Grade 2. Learning to run is Grade 3 and so on it goes.
You asked if you still have to learn all the Grades before proceeding to G5.
Let me ask you if you can jump without learning how to stand, how to walk how to run and so on.
I guess that answers your question.
Learning music is a cumulative experience. You learn 1 skill and then 2 skills and then 3 skills etc.
Initially you learn to recognize triads(simple 3 note chords). Then your hearing improves and you can recognize 4 note chords (Maj 7, Maj 6, min 7 etc). Then you learn to recognize 5 note chords(9th chords etc). More advance and you move on to altered chords like b5#9 etc.
How can you recognize altered chords when you are even clueless when it comes to triads?
How can you proceed to Grade 5 when you haven't even learned the easier stuff that is Grades 1-4?

It does not matter how old you were when you started out on your musical journey. Its for your own enjoyment. Why be envious of others who had an earlier headstart or are more talented than you?
Would you be jealous of Richard Clayderman because he can play better than you?