You'll find very slim pickings on Vinyl, there has been an ongoing explosion of interest in Shostakovich from the 1990s onwards - but that was after classical music stopped being released on vinyl.
Basically for the 5th you will be limited to a very small selection of recordings, they are all good if you can listen past the scratches and surface noise!
Andre Previn/LSO on RCA
Leonard Bernstein and New York Phil on CBS, and also with the LSO on CBS
Eugene Ormandy/Philadelphia on RCA
that Skrowaczewski/Minnesota recording above
and possibly some Eastern European and Soviet artists on Soviet-era recordings, eg Kyril Kondrashin and Karl Ancerl.
For the tenth - even more limited -
Herbert von Karajan and Berlin Phil 1967 on DG - a wonderful performance and about the only contemporary music in Herbie's repertoire, it was re-issued in the 2000s on 180g vinyl by Speakers Corner (I have two copies and will never part with them
)
Eugene Ormandy and Philadelphia again, on CBS I think. Ormandy also made good recordings of the 4th and 15th symphonies which you may get lucky with.
Karl Ancerl/Berlin Philharmonic- 1960 and MONO sound.
All of the above are available on CD.
But... there are many great modern recordings in good scratch free sound! In particular I'd point out Rudolf Barshai's excellent complete set on Brilliant Classics - a top notch German Radio Symphony Orchestra conducted by one of the composers' closest musical collaborators (he was the violist in the Borodin Quartet for which Shostakovich wrote many of his 15 quartets) - and in very good sound too. As a starter it can hardly be bettered at the price.
https://www.amazon.co.uk/dp/B00005UW2B/?tag=pinkfishmedia-21
Beyond that there are a myriad of great modern recordings - Vladimir Jurowski, Neeme Jarvi, Mariss Jansons, Bernard Haitink, Mikhail Pletnev, and many others. Of particular note, the still ongoing cycle from Andris Nelsons and the Boston Symphony have all been excellent performances in fantastically good sound.
https://www.prestomusic.com/classical/search?search_query=nelsons shostakovich boston