Are my €5 bills (2013) counterfeited?

I noticed that out of 5 bills of €5, none of them are perfectly aligned. The shiny strip is off on each one of them, each in different ways. One is completely shifted to the right, so that the black lines even overlap it. Then i started comparing the left side of the notes, and some of them have a thinner “border” than the others.

These are just random notes I saved. Is counterfeiting rampant, or can't the ECB print identical notes? None of them look perfect, none of them are identical.

Look okay to me.  I am not sure what the problem is.

Have you ever seen how many notes are printed & the speed the sheets are fed through the machines? It is a pretty fast, yet a complicated multi-stepped procedure. Check out a youtube video (they will only show portions of the production process for security reasons). Then you may understand small variations such as the ones you are probably seeing. 

Remember the golden rule: counterfeiting may be “rampant” but 

A) most notes that are copied are high denominations (€100) to make it worthwhile for the criminal organization (your 5 bills of €5 would not qualify)

B) just take a magnifying glass and look at the fields (where the microprint/Orion circles are) & if they're not blurry, its likely original (the real deal)

C) any bogus nots seems like rampant fakes to the one stuck with it (the owner loses the amount of money so its painful) but in reality counterfeiting is a lot less rampant than digital crime & money laundering. There's an incredible anti-cash movement that is very successful in getting more people hooked on Credit, VISA, etc. 

I just never realized before they made them this sloppily. The tolerance on alignment seems to be at least 2mm either way (spread: 4mm) and I didn't go looking for these…

I don't think they will actually phase out cash – that would spell the end for too many criminal and laundering schemes, black markets, etc... I don't really get why they're contradicting themselves, on the one hand with cashless society propaganda and on the other hand announcing a new € note series.

The two notes you are comparing are note from the same print run, or from the same printer (indicated by the group of small letters and numbers on the right-hand image). They could have been printed millions of notes apart from each other, and at different ends of the continent. It would be unreasonable to expect them to match precisely.