Questions: 1950's Proof Sets

From 1950 to 1955 they came in the type of cello packets stapled together like you describe in a small box. There are two types of packaging for 1955. Envelope flat pack or box.
The yellowish brittle cello are the original slips and they became brittle over time.
Some dealers will move each coin into a soft same size "baggie" and staple them together with the box because it will be more presentable to buyers than the deteriorated cello and often rusty staple.
The boxes have value even without the coins and it might be best to save the box and put the 5 coin set in a Capital Plastics Proof Set, screw down holder.
Handle your coins by the edges of course.
Some ugly toning has occurred on some stored in the boxes and original cello and sometimes you find attractive toning. Often a mix of both on the 5 coins. Blackening is common.
Hope you have some cameo examples. 1950 and 1951 sets are pretty expensive and they go down from there. Cameo proofs and especially certain cameo Franklin halves make a considerable difference in value. Condition of the original surfaces is important as well as "eye appeal".

Don't clean them!
Many sets for sale are assembled one coin at a time that you'll see already re-packaged in Capital Plastic holders or 2x2 singles and have been "dipped" in coin cleaning solutions. They didn't always come from the same boxed set.

Lets see some nice clear pictures of your sets.

Well TNG, pretty much said all that could be said about care and storage of these sets.

The several '50's sets I have (both box and flat packs have not turned like your have, I'm curious to see what your looked like in the original cello pack and after you moved them.

I agree. Who knows when or what little coin baggies were used to replace the cello ones by dealers or collectors? I remember seeing cello replaced by coin baggies all the way back to the late 70's and not necessarily for just the proof sets in the box. I've seen single coins of all kind in them.
This is a good reason to just change them out into Capital Plastic screw sown, 5 coin, proof set holders.

I'd flatten the staples and place the 2x2's in the original box. For the flat packs, you could use archival bags about the same size and use a common food vacuum sealer to separate and protect them.