I have made a test and reached 5020 items in a list. I get this message in the list settings 'The number of items in this list exceeds the list view threshold, which is 5000 items. Tasks that cause excessive server load (such as those involving all list items) are currently prohibited.'
I can still add items to the list, however the above message sounds threatening enough. Do you know if Microsoft has got alerts on their end and might decide to restrict throttling or other parameters on the tenancy?