The Wikipedia article mentions that he studied at the University of Manchester and the Royal Manchester College of Music (now the Royal Northern College), but it does not say who with, just that his fellow students included Harrison Birtwhistle. Later he studied at Princeton University with Milton Babbitt and Roger Sessions. His training and early aesthetic allegiances were very solidly within the high Modernist tradition therefore. But, as with so many other English composers, he was not entirely consumed by it and also absorbed considerable influences from Medieval and Renaissance traditions, especially English ones.
So it is not entirely surprising to see him following his early avant-gardism with works that, at least in their titles, refer to established genres like the symphony and string quartet. Interestingly, Davies picks up on perhaps the last of the great symphonists (outside of Russia, that is), Jean Sibelius. There is a YouTube clip of Davies introducing and conducting the Finnish master's Symphony No. 6.
The symphony is in one uninterrupted movement about 25 minutes long, though this is divided into a number of sections. Without the score I can't do any analysis (which would take a great deal of time, in any case), but we can let our ears be a guide. Though the music is not exactly tonal, it is not exactly atonal either. There are tonal centers which include C# and G (a tritone apart). Though I have not read any theoretical discussions of Davies's style, it seems to me that he might approach tonality in a way vaguely similar to the way Bartók did: transforming some traditional structures through replacing perfect fourth and fifth relations with tritone ones. Rhythmically, of course, they are very different.
The Symphony No. 5 of Davies is quite listenable, though very moody and dark. Here is the composer's own program note on the music:
The Symphony is based on material from my youth orchestra piece Chat Moss (1993), but behind both pieces is a hidden source: two plainchants from the Liber Usualis - the 'Haec dies' Easter music and 'Domine audivi' from Habakkuk 3:3. The music of Sibelius, in particular its possibilities of self-generating form, was also central to my thinking, having recently studied and conducted Sibelius's Symphonies 6 and 7 with several orchestras.The symphony would seem a good choice for today then, Easter Sunday. So, let's have a listen. This is the Philharmonia Orchestra directed by the composer: