Hi, sorry to read about your miscarriage, it seems very hard over Christmas.
In answer to your question, sorry but, yes 5 days after sex it is impossible for a positive test from a new pregnancy, implantation would not even have occurred at this point even if you had ovulated at the time of the sex.
So it would appear your hcg levels are still going down. I have had a couple of miscarriages where it has taken 6 weeks for levels to drop, even from around hcg of around 2000. Technically hcg should halve every two days, but it does not always happen if there is retained products of conception.
Since you are feeling ill, I think that you should check if you have any hint of a fever, and if your temperature is raised, then urgent medical attention should be sought, in case you have an infection following the miscarriage.
Having said that, on many of my miscarriages my "morning sickness" was much worse while hcg falling following miscarrying. I can empathise with this being hard emotionally as well as physically.
Just so you know, it is possible to get pregnant while there is hcg still in your body. I have ovulated while still getting positive pregnancy tests (wierd!). I have also become pregnant immediately following a miscarriage, with no period in between. So it is not impossible that you could still get pregnant before your next af, and if you ovulated around the 10th it would not be impossible for you to be newly pregnant again, but it would just not show up yet on the test as implantation could not have occurred after only 5 days, but would soon if it is the case, and would give even more confusing hcg results.