Congratulations, piano learner, and well done. (And can I have a glass of that champagne, please, Motrax).
Should you skip grades? As with everything in the universe, it depends. So what follows is just my opinion.
Yes. By all means go straight to grade 5.

Why?
1. These are exam requirements to ascertain your skill/progress. They are
not a methodology to learn the piano. If you simply follow the grades’s requirements in order, you will not really end up playing all that well. Besides it is arguable if the order of technical and theoretical material is the best or even desirable.
2. Take the case of scales and keys. Technically, one should always start with the B major scale, a scale that in the exams is only required after grade 3. If you follow the idea that you should use the exam syllabus as a pedagogical guide, you will only start the B major scale after three years. Surely this cannot possibly be right. Personally I have my students working on scales so that they know all the 24 of them (plus the theory behind it) in the first 3 – 6 months. It is not that difficult: if you dedicate 10 – 15 minutes a day to scales you will know them all in that period of time. And this of course is the requirement for grade 5. Why exactly are you going to trudge along for five – six years when you could be there in 5 – 6 months? We, old students may not have that long to live!

3. The repertory for grade 4 and below is usually dismal. At grade 4 it starts to get better, but at grade 5 there are superb pieces (both in the syllabus and just in the piano repertory in general).
4. You do not need to do the grades in order. There is no rule that says so. You are allowed to skip grades. So why not?
5. You will save money (although the exam is not that expensive so this is not really a major reason).
6. Being an adult you should be able to learn the stuff in a fraction of the time it would take a child. Think of the resources you have that a seven year old does not: You can buy books on the subject. You can watch DVDs (and have the economic power to buy them) of all aspects of piano learning / performance. You can participate in forums like this one. You can buy CDs of the pieces you are interested in and compare different interpretations an music form different styles/periods (which is more or less what aural exams are all about). You can delve in your interests without having to do some silly homework from school (although you still may have to do the silly work from your job). With all these resources (and possibly more) at your disposal, why should you trudge along at a snail pace?
it is not necessary. You can actually “talk” intelligently with your teacher and work on the information he gives you, something a 7 year old usually cannot.
7. The syllabus is valid for a full two years. Are you telling me that in two years it is not possible to attain the necessary level to pass a grade 5 exam? If you feel like Percy5129 that it is important to follow the particular order the subjects are presented in the exam syllabus, by all means do it (but it is a very inefficient way to go about it), just make sure you are prepared for grade 5 by November 2006. And by the way, take the grade 5 theory exam at that point as well.
I hope this helps.
Best wishes,
Bernhard.