Shostakovich composed this symphony in 1937 and it has remained the most popular of his 15 symphonies. The melodies and harmonies are certainly more accessible than in some of his compositions. There are several recordings in the catalogue but the ones with which I am most familiar are those by the Chicago Symphony Orchestra conducted by Andre Previn and that by the Concertgebouw Orchestra under Bernard Haitink. I think both of these are fine interpretations, though Haitink is better at bringing out the drama. In some passages Previn interprets the work more as if it had been composed by Rachmaninov. But I have listened to both performances many times and would not want to opt for a preference.
The Haitink recording has the advantage that it is coupled with the 9th Symphony, played by the London Philharmonic Orchestra. This was composed in 1945 and is a much lighter work than its immediate predecessors, the 7th and 8th Symphonies which are full of portrayals of the torments of war. The 9th is a positively joyous symphony by comparison, though in no way frivolous. The Decca recordings of both symphonies are crisp and clear and a delight to listen to.Shostakovich: Symphony No. 5 in D minor - Andre Previn: Piano Concerto No. 2 in F - Paavo Berglund. (HMV Classics, 1992).