That depends on the question..
The courses themselves; Level 3 & Instructor should only take about 10-15 days total.
The real question is are you prepared for them?
I highly suggest (to everyone) that you don't take the level 3 or instructor courses if you cannot already do the physical requirements. If not, your instructor will have to spend too much time on your 'training' and you will miss out on the key components of the actual courses.
So back to your question, 5 weeks is enough if in that time you can COMFORTABLY reach 40m, do 5x20m with 1:00 recoveries, rescue someone from 25m, do 4:00 static, 75m DYN....
If for example, you've already been training for a while and still struggle do to 30m, then no, 5 weeks probably isn't enough time to train for and complete those two courses in a way thats most beneficial to you. I think the biggest disservice that Instructor candidates can do to themselves is take the instructor course without already being comfortable doing 40m.. Not just capable, but comfortable.