I taxed my ST without having the propper V5.
I bought the car with 2 weeks left. Went to the Post Office with my new insurance certificate and green slip and taxed it there and then. Now im £215 lighter. You can only do this 2 working days before the end of the month. Then I got my propper V5 about a week later.
If you only have the green slip of the V5, your not supposed to do your tax online as it will most likely go to the previous owners address. Its cheaper to do it in the P.O anyway, you get charged £2.50 for paying on credit card online. But then, you can only pay with cash, cheque or debit card at the P.O.
Andy