i have a 95 gs300 and when i jumpstart it the car runs for about five minutes and then the car dies. the battery i good and the alternator is putting out 13.5 with a load. the main fusible links are good and i cant figure out what the problem is. please help me.

Are you getting any warnings/indications on the dash when the car runs?

Do you mean the battery is going completely flat again and won't restart unless you jump start it? I would expect higher than 13.5 volts from the alternator too, more like 14.2 so it may not be working too well. How do you know the battery is good?