Just a note, if done right you can travel that 5000ly in 30 minutes gametime (1kly = 6 minutes).... Does require a lot of engineering and for the average player not possible. However, with an average ship (say the AspX) and decent engineering (+50% FSD)
to get 50Ly that's perhaps 32 jumps using neutron stars, at a non optimal rate that's 45 minutes odd. If you self destruct back thats gonna cost you 2 million in insurance and another 4.5 million if you buy then sell the ship after.
For the cash savvy cmdr you can fit a discovery scanner and do the route out and back, sure it takes twice as long but you'll probably earn 300-500k Credits on the way, if you don't yet have the cash for an Asp the Adder
can get 36ly in a much cheaper package which will need about 42 jumps total, 1hr again if you aren't rushing too much.
Best case you can do a jump every 53-60 seconds(ish) but that's record racing speeds.
^ For more tips see the Buckyball race team, they taught me a lot when I set out to beat some of the records but the neutron highway is the way to go for distance travel
As for the unknown fragments you didn't need the corrosive cargo rack. Fragments are materials and are not stored in cargo. You probably found the Thargoid probe or artefact. The Probe doesn't help afaik but either shooting or better yet ramming the artefact to death drops 2-3 fragments which go into your materials storage to deliver to Palin.
https://www.youtube.com/watch?v=IabpaGfXQAs < Note not all crashed ships are still there, some mysteriously disappeared, so don't take co-ordinates/planet as gospel
I totally get where you are coming from with the disappointment of loosing exploration data and I totally understand the confusion around the fragments and that. Sounds like you got off on the wrong track and it just got worse and worse there. I think the exploration distance for Palin will stick even after death but the fragments obviously won't. Hopefully the above tidbit of info will help when you come back to it. For what it's worth the Thargoid probes are a pain, I did Palin unlock back when they were rare and the only way to find one was to sit in supercruise for a few hours waiting for the right deep space signal source.
If you come back and fancy a hand and or a bit of a leg-up with some help trading/fighting/mission-ing etc let me know!

(PC, Uk timezone, same name in game but no space, usually on at weekends but can be persuaded to join in evenings after work if pre-arranged meeting time/location)