Change a personal Facebook account to a page.
The nature of this questions is shaky.
Do you want an entire strategy outlined here?
Are those 5K friends relevant at all? Are they targeted and engaged followers?
With organic reach so low, I wouldn't be excited if those 5K people went straight over to his fan page.
In the end, what does that mean?
(Ok, enough rhetorical questions )
My advice is to lay out a strategy that actually helps the client reach his/her goals rather than simply "change to a page."
I would create that page asap, outline a content strategy, and deploy an ad strategy to get super-specifically-targeted people into the pediatrician's funnel.
(Plus, it's always helps to show quantitative results to clients. Email addresses are almost as good as new patients. If you're super savvy, you can actually convert those new emails addresses into patients for him/her.)
Start by getting enough likes to advertise.
Start advertising "shareable content" like helpful info in picture format. (People will share and engage with this)
If there are blog posts to promote, promote those and pixel your visitors.
If you can organize some sort of Facebook event or virtual giveaway, that will be a great way to generate quality leads for a pediatrician.
(Again, pixel people every chance you get so that you are able to re-target them and keep your marketing message in front of them.)
The most important thing here is to stay focused on delivering tangible results with social media services.