Is it normal to have dots remaining on your face from prp injections after 5 days? (photo)

Yes it can be.

Some bruising is normal with an intensive manual prp technique and some people will bleed more than others, even with a small needle and superficial technique. You can eat pineapple which has bromelain an enzyme that can help the body clear out the blood causing the bruises. Some also recommend arnica montana which is a homeopathic product. Some providers offer a laser treatment such an NdYAG laser will is a vascular laser and will break up the blood deposits to speed up the disappearance of the bruise.
Also  I would d avoid the sun and wear protection to prevent staining of the skin (which could show up as dark dots) called hyperpigmentation (or post inflammatory hyperpigmentation). As the skin heals it is more inflamed than the surroundings and is more sensitive to the sun, so it can 'stain' or tan unevenly
I hope this helps :)

Needle marks usually disappear pretty quickly sometimes in a matter of few hours, but may last for a few days in some patients. There are also patients who are prone to develop hyper-pigmentation, although not common with needle marks, it is theoretically possible. you should consider checking with your provider to be sure.