iphone 5 is not updating icloud.

Go to Settings>Mail,Contacts,Calendars>Default Account (in the Contacts and Calendars sections). Do you have the Default Account setting there, and if so, what is selected as your default account?

Then that isn't the issue...

Have you tried adding a test calendar event and test contact on both your phone and Mac, then checking icloud.com to see which, if either, appear there? If not, I would suggest doing so as that will help narrow down which one is the issue, or confirm that it's both of them.

Get on your Mac and go to icloud.com. When you next come back Randers will like to know if icloud.com looks like info on your Mac or on your phone. The device icloud.com emulates is talking to icloud and another device is having problem.

As fromsouth said, check icloud.com to see if the data reflects your Mac or you phone, and if either the test contact or calendar event you added from either your phone or your Mac appear there.