Are you doing any prep work? Doing the door jambs removing the door seals and pulling the windshield and chrome finishers on the windshield post? Think about all of the time it takes for proper disassembly and reassembly. What's your expectations? Is there any other areas of work needed that should be addressed when the work is done?
Don't expect a good job for $5000.00. Cost of paint and materials and shop overhead would be reasonable at $2000.00 before you factor in technician labor.
Painting is just part of it. Proper stripping and body work even assuming no rust repair are the thing sometimes we may overlook that are really what you will see when the job is done.
Really good shops may quote by the hour, provide a low to high range or keep it somewhat open ended until its down to metal to be able to fully ascertain all of the needs to do it properly.
What about the hardtop, and if so how far apart will you take it or will you just tape it off?
These are the kind of questions you should ask yourself.
You can spend 8 hours per door just installing new rubber seal in itself and another 8 hours or so stripping prepping fine lining and refinishing 4 hub caps.
It's an amazing commitment and amount of expertise and work to do the job right. Sometimes making a deal for too low of a price can backfire on yourself in the shop putting the project on the backburner and taking too long and cutting corners. Go to an experienced shop who can provide references for this kind of job.
$10000 on the low side without going too deep would be a gift and up to $20000 or more can be easily justified.
These days with rising prices of these cars what you put into it will increase the value of your car if its done right.
The only place I saw close to you area that appears to specialize in W113 to name few is Aventura Motors, however I have personal connections references or any feedback on them.
http://www.aventuramotors.com/site/index.php?route=product/category&path=61_69A little further out in CT is a well known shop call Automobile Associates. I have seen their work. It's incredible.
http://automobileassociates.com/home.htmI hope this helps.
Regards
Peter