Members of this race gain resistance 5 against negative energy damage. They do not lose hit points when they gain a negative level, and they gain a +2 racial bonus on saving throws against death effects, energy drain, negative energy, and spells or spell-like abilities of the necromancy school.
This armor protects its wearer from harmful negative and positive energy, including channeled energy. The armor absorbs the first 10 points of positive or negative energy damage per attack that the wearer would normally take. The wearer has a 25% chance to ignore negative levels from any attack. Deathless armor does not block healing of any kind and does not protect against positive or negative energy effects that do not deal damage or bestow negative levels. The deathless ability can be applied to armor of any sort, but not shields.
Regarding these two subjects, would they stack? If not, which parts would override and why?
Energy resistance doesn't stack you only get the higher value. The rest of it would stack.
That would make sense if both of the texts say that it's classified as energy resistance. The Racial Trait says it's energy resistance, the Armor Property doesn't. The way the RAW is worded, the Armor absorbs the first 10 points. After that, the armor stops functioning, and at that point, the character's 5 resistance applies.