How are you measuring your heart rate? Are you doing it with a heart rate monitor? If so, I think your heart rate monitor is malfunctioning. If you are measuring it yourself, you would have to be feeling 5 heartbeats per second, which is impossible to feel. I truly don't think your heartrate is going up to 300 bpm. If it was going that fast, you would probably be unconscious. Have you had a holtor monitor (24 hour ekg monitor) to truly see what your heartrate is doing throughout the day?
Have you seen a cardiologist? Also, what do you drink or eat after exercising?