You are technically out of date to make any claims for 2005/06 and 2006/07 as you will see from here
. The tax office is under no obligation to accept tax returns from you for these years.
Given that you did not complete a tax return for either of these years, you are also out of time to make a claim under the overpayment relief provisions as you will read here
There is a form of claim called overpayment relief special relief which you can read about here
. Such a claim is only possible if the tax office raised determinations for the tax years concerned which I doubt as you only mentioned one for the 2009/10 tax year. I'm afraid that in the absence of determinations, this avenue is also closed to you.
Given that the tax office caught up with you in 2012/13, the only thing I can suggest you do is to make a complaint in the form of a letter in which you set out the sequence of events and make the point that at no time were you warned about time limits for submission of tax returns, particularly in relation to years where tax may have been overpaid and the time limits were approaching or had even passed.
The tax office will need to look into your complaint but I have to say I'm not confident that it will help you at all. The time limits are there for a reason, they apply to every taxpayer and every taxpayer is ultimately responsible for keeping their own tax affairs in order. It doesn't help that you have little information to be able to complete tax returns or to provide to the tax office and they probably won't be inclined or even be able to track down CIS tax information for you as far backs as you need it. You can read about the complaints process here
but I'm afraid that you are likely to be wasting your time and will have to chalk it up to experience.
I hope this clarified things for you but let me know if you have any further questions.