i agree with Rusky.
I think you should see your GP. yes, you're unfit, but you did have some pretty strong symptoms for a 5-10 min ride. It totally could just be because your not used to exercise so I'm not saying anything is wrong with you and you definitely should not give up, but it wouldn't hurt to just have a check with the doctor to make sure there are no underlying medical conditions, particularly because of the metallic taste (which could be anything from simple stuff to other conditions). For instance, you could have high blood pressure, and if it's high before you start, then it's REALLY high while your exercising (and being unfit can mean high blood pressure). This might explain your extreme dizziness and why it took so long to recover. If this is the case, the doc will give you some medication to bring the blood pressure down and you can carry on exercising (and if you have got this, that is a very good reason why you should be exercising so don't give up). But like i said, that's just an example and everything could be fine. If everything is fine, carry on as you were and you will be amazed at how quickly you will build up the mileage. If everything is not fine, take the doctors advice on how much you should do and how quickly you should build it up.
As said, measure your improvement by your distance and fitness levels, not by how much weight you lose. you will find it more motivating this way and more unlikely to be focussed on losing weight, and all the negative thoughts it can bring.