If you go back before the 2004 Directive there was a system of residence permits that did indeed need to be renewed every 5 years and there was an expiry date on the permit. They varied, some were blue and some were green, although I am not sure of the significance of the different colours.
When the 2004 Directive came into force in 2006 the system changed to a Residence Certificate, which is beige, and a Permanent Residence Certificate, which is is blue. The beige certificate does not have an expiry date on it and there is nothing in the Directive about renewing it. As far as I am aware the only reason to renew it would be if your status changed. For example someone might arrive as a student and obtain a certificate under that paragraph of the Directive. When they completed their course they might then get a job and apply for a certificate under that paragraph of the Directive. Alternatively someone might arrive here to work and obtain a certificate under that paragraph and then retire and become self supporting and so apply for a certificate under that paragraph.
This extract is from a Document Issued by the UK Government
on the basis of advice issued by the Greek Aliens' Bureau:
The following information has been supplied by the Greek Aliens Bureau:
It is obligatory for all EU nationals to apply for a “Registration Certificate” (Veveosi Engrafis - Βεβαίωση Εγγραφής) after they have spent 3 months in Greece (Directive 2004/38/EC). This certificate is open-dated. You only need to renew it if your circumstances change e.g. if you had registered as unemployed and you have now found employment
The link is a pdf so it should download to your Downloads folder, not open in your browser. There are a lot of contact numbers in it but not for Crete. You could also try contacting the Embassy in Athens and asking them if they could send you a copy of the advice issued by the Aliens' Bureau.
PS There is a classic Catch 22 situation arising in the UK. Suppose you are an EU National working in the UK and you make a small mistake on your tax return. You realise the mistake and correct it but Immigration picks up on it and issues a deportation order on National Security grounds. You do not respect UK legal processes so you are an undesirable alien. You lodge an appeal, on the grounds that it was a genuine error that you have corrected and there is no outstanding issues with HMRC. The appeal reinforces the deportation order because appealing against a Home Office decision is yet further evidence that you don't respect the UK's legal processes.