Re: GH5 prime lens set-up
I don't get your budget. Very expensive camera, inexpensive lenses?
I know Panasonic is video oriented, but I don't understand their lenses; all fly-by-wire makes it impossible to follow focus.
The m43 advantage is that you can use other format lenses with an adapter.
For native m43 lenses, consider the Olympus PRO lenses or primes with manual focus clutch; although these are still "focus by wire" you get repeatable focus with them.
Or, you can look at the Voigtlander manual focus lenses. They have 4 (10.5mm, 17.5mm, 25mm, 42.5mm). If limiting to 3, then the 17.5, 25, and 42.5 make a good set. Of course, each one is more than your lens budget. All are f/0.95; very fast for m43.
Another option is a speed booster and FF manual focus primes. I use a Metabones 0.71 speed booster and a straight adapter, so each lens does double duty in focal length. Then you can get some good used Nikon AI-s D lenses. They tend to have the same filter thread diameter. I have a set of 20mm, 24mm, 35mm and 50mm. You could drop the 35mm because the speedbooster with 50mm is similar, but I like the speed advantage of the speedbooster with each lens.
The speedbooster will blow your lens budget, so you could get a plain adapter and the lenses, and add the speedbooster later. That is, in fact, what I did. The lenses are available used for very reasonable prices. But I don't think 20mm is wide enough to be your widest focal length.
What's cool about the nIkon lenses is that the focus rings on the 24, 35, and 50mm lenses are the same diameter, so you can use one gear adapter for all three. That will same some money until you can afford to outfit each of them.
If you are firm on your price, then I recommend a used Olympus 12-40 f/2.8; it has the manual focus clutch for repeatable focus, covers the most usable range, and is relatively fast for m43.