Hi there and welcome
No they are not for real, it is a scam. They try to get onto your computer and obtain your credit card details.
They then make these huge charges to it and at times sell the credit card number off to other companies to exploit
In addition they try to get personal information from your computer to use for future scams against you.
I strongly urge you to not provide them your credit card details and if you did contact your card company asap.
And do not allow them on your computer (they will have to get you to install a program). If you did this, tell me please.
If they call again, do answer it, but tell them you know they are a scam and your going to report the call. This will stop them sharing your phone number with other organisations to try other tactics.
If you would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.