Have people here had experience with being recruited by a headhunter for a position they are pretty sure they are unqualified for? What was your strategy?
This has happened twice for me recently and both are positions that fit in line with my work, though usually require or prefer 3-5 years more experience than I have.
First, how did you determine you are unqualified for the position? How well do your skills fit the position? Somebody else looked at your resume, paper or something, looked at a position and determined that you might be a fit candidate. So the answer to the why you determined you were pretty sure you were unqualified is key to the rest of the discussion.
If its years experience, see is my take below. If it is other issues, then that needs to be discussed with the headhunter. You need to discuss whatever it is that made you reach your conclusion that you are not qualified vs what the headhunter saw or found out about you makes you a possible fit for the position proposed. Headhunters generally get paid to put someone in the position, so they really don't want to send a candidate who is unqualified. Puts the headhunter in a bad light with the potential employer, less likely to be listened to about next candidate, position etc.
Is the position is just "preferring" 3-5 more years experience, or is it stated as required? If just preferred, I would just go for it, unless that number is like double or more your actual experience. That is, if you have one year exp, and they want 4-6, that might be a big issue. If you have say 15 and they are asking for 17-20, its really a no never mind.
If it really is a requirement, discuss with the headhunter and make sure they understand where you are in terms of experience versus the position requirements. Find out if there is some substitute for experience.
Most companies look at jobs in three or four big classes: Newbies, who will need significant mentoring and aren't ready to do a lot on their own; journeymen, who can do most jobs without handholding, and know enough to know when they are in over their head; and senior/expert, who can do the job, figure out the weirder issues in the field and have knowledge and skills to be mentoring more junior people. Some places separate those with no experience from those with a little experience (0 vs 1+ years).