Implantation bleeding can sometimes occur a little bit after actual implantation occurs. Well, the bleeding itself occurs when implantation happens, but you might not notice it until it comes out, which can be a day or two later. But if you have already received a positive on a test and you are past about 12 dpo, no I wouldn't suspect any bleeding you get at that point is implantation bleeding. It's rare for implantation to occur past 12 dpo as your body likely won't keep your progesterone high enough to make a possible pregnancy viable much past that without implantation occurring. You might get bleeding at 5 weeks, but it's not due to implantation unless you ovulated quite late. I personally wouldn't consider first tri bleeding that occurs because of normal uterine and hormonal changes to be 'implantation bleeding' as that can happen throughout first tri and isn't related to implantation as that's a very specific event. I'd consider implantation bleeding to be what happens at or just after implantation and I think that's usually how the term is used. Bleeding isn't necessarily a bad thing. I had very heavy bleeding in 1st tri last time at about 10 weeks which they couldn't explain. All was fine though. That baby is now a 4 year old. So bleeding can be normal throughout first tri, but no I wouldn't suspect that bleeding at 5 weeks after you've already received a positive test at home is implantation bleeding. It sounds like your doctor maybe just wanted to be reassuring though and was trying to say that bleeding can be normal, which is true.
I've been here too long and was taught by fellow bnbers 
