That is a truly lovely Dart my friend. You should feel quite thankfull to have it. I'm sure it was not gotten that way easily. If it is a "survivor", that is unrestored, then you are even more fortunate.
I have had dot 5 in my brake systems for years. I like it, and would do it again. I have never had a problem with it, and it stays clean and clear much longer then dot3-4etc. It is incompatible with anti-lock brakes and automatic traction control systems however, so it is mostly useful for older cars. I had a modern Corvette for awhile with all the elecronic bells and whistles and you could not put dot-5 in it.
As I understand it, the Dot5 is most useful for cars that are not driven much, but just sit in the garage and go out on weekends. I took my car to a shop with a power flush, and had them flush the brakes, and follow up with the dot5 install. I never had a problem. Pedal has felt great, right from the start. I did it simply because the dot5 doesn't raise hell with the paint around the MC. AFter working hard to restore the cars, I didn't want DOT-3 brake fluid messing it up. And mess it up it will.
On my '70 DArt, which I have since sold, I laid a spare tire in the spare tire well. This tire had been on the car when I had bled the brakes with dot-3. The residue on the tire from bleeding the brakes, which had taken place years earlier, ate the high-quality hardened urethane paint off the spare tire well bottom.
You can do what you feel you need to of course, but I don't think I would try to bleed the brake system of Dot-3 and follow it up with Dot-5 myself. It doesn't cost that much to have a shop do this. They get annoyed at me anyway because I do almost everything myself. I typically take work to the local shop which doesn't make them much money. I do all the real money makers myself. It is nice to once in awhile throw them a bone of some kind and pay them to do something. Not only that it gives them a chance to ooh, and aah over your old gem.
Sam