The usual convention is that 00:00 refers to the start of a day, whereas 24:00 refers to the end of that day. So, according to that convention, it's midnight on the 4th.
I feel the need to disagree with Chris (the first time?). If 24:00 refers to the end of the day then 00:00 must be the start of the next day, so the 5th.
23.59 is the final minute of the day and 00.00 is the starting 60 seconds of the new day. For example New Year's Eve counts down the final 10seconds of 11.59pm. When it reaches 00.00 it a new day and new year.
I'm sure it ends at midnight at the end of the 4th November. which is the same thing as 00.00 on 5th October.
It would be clearer if it was shown as ending at 23.59 (and maybe 59 seconds) on 4th Oct, but maybe they want cover to run for exactly a year and it started at 00.00 on 5th October 2010
If 00:00 is the start and 24:00 is the end, does that not mean it must be 00:00 AND 24:00 at the same time? Otherwise as soon as it shows 24:00, it would tick over to 00:00, time will have passed but not according to the display. I'm sure most would have put 23:59 to avoid any confusion.
factor30 - I'm struggling here to work out how midnight on 4th November is the same as 00.00 on 5th October. I'm pretty sure there's a months difference there! lol
Anyway, why not just contact the insurance company to find out for definite.