Hi Walamob,
You're obviously not as old as me. If you were, you would be able to remember (as I can) the days when ALL cars parked by the roadside (even if they were actually on the grass verge) had to display lights at night. (I'm thinking back to my school days in the 1950s and '60s). The way this was usually done was that car owners had paraffin lamps which showed white to the front and red to the rear. These lamps were hung on the side of the car.
Although that was a long time ago, most of the law which applied then still remains in force. (i.e. vehicles, parked on the public highway, must normally display lights during the hours of darkness). The only change, that has come about since those long off days, is that there is now an exemption for vehicles which are parked in a built-up area (with street lighting), where the speed limit is 30mph or less, and where the vehicle is facing in the direction of the traffic flow. (i.e. the vehicle must be parked on the left side of the road, except in one-way streets).
Unless that exemption applies, you must always ensure that your parked vehicle displays lights, during the hours of darkness, when on a public highway. How you do it is up to you. (You don't have to rely on paraffin lamps any more. You can get rechargeable parking lights these days). If you don't do so, you will be committing an offence.
Legally, you haven't got a leg to stand on. You might find that the authorities would take a compassionate view if you advised them that the vehicle wasn't deliberately parked but had broken down. However, you might also need to explain the reasons why you didn't get the car moved for 5 days.
Chris