The average UK petrol price is now 137.08p a litre compared with 132.01p in the second week of January, the AA said.
Since early January the price of diesel has gone up from around 140p a litre to 143.96p a litre now.
The AA said it was the third time in less than 12 months prices had gone up by 5p in little over a month, following price rises in March and October 2012.
The AA said there was now a chance motorists would cut back on car usage. It added the 5p-a-litre increase put £2.50 to the cost of filling a typical 50-litre tank, or £3.50 to fill up a Ford Mondeo.
A family with two petrol cars was now spending £10.62 a month more than at the beginning of the year.
AA president Edmund King said: "A weaker pound has probably contributed around 2p a litre to the increase."