First off, the Discovery 5 dictates you must use synthetic. So that is what you are using. If you put dino oil in the engine, that'll be a problem.
I think there is a Mobil 1 oil that'll work with the gasoline engine version. But also, plot twist, check your local dealer. OEM oil at my dealer last I saw was $13/quart. Not bad, not great. For me its worth it to get the ACTUAL OIL for the engine. Considering how specific the oil requirements for the newer engines are. Its nice to not have to pay shipping on fluids.
Don't cheap out on filters. Once again I think LR has ok pricing on OEM filters but also Mahle is a good brand. I think Mahle might be the OEM supplier so that is fine. Also Fram is basically the devil so don't do that.
Also get the vacuum oil extractor. Works great. Will make oil changes a breeze. I love using it on my dad's LR4 and my D5. You'll spend less than $100 on the oil change and it'll take about 30-45 minutes. Cheaper and probably quicker than trying to take it to the dealer. And yes the vacuum oil extractor gets ALL the oil out the same as dropping the drain plug. The only way to get more oil out would be to drop the oil pan, but we aren't doing that. Also its so nice to not have to get under the car and have hot oil explode everywhere (I'm looking at you, LR3...).
Also on the newer engines, lore has it to change the oil every ~7,000 miles or so. Which is still pretty good.
So this should be a good path moving forward to maintaining your D5 engine. Or not. Do whatever. I work in the engine industry and its fun when the customer never changes the oil/uses crap oil/uses crap filters and then wonders why the top end explodes or the bottom bearings commit suicide. So I'm a bit sensitive to having the "you killed your own engine tough cookies" conversation because no one wants to take responsibility.
These engines are great if you take care of them.