As stated above, the +5 Death means the weapon will do elemental damage of 5 death to enemies it strikes. (For clarity, Warrior Skill whirlwind doesn't add the elemental damage). Greataxe of Falling stars also has the Beast Killer attribute, so it does a little extra damage to beast type enemies (wolves, minotaurs, my ex).
You'll come across loads of weapons that do elemental damage. From the +2 Fire damage for the Vulcan Dagger, to the +10 shock damage of the end-game Pneumatic Mattet. Being mindful of the extra damage can help in winning fights as enemies can have a range of weaknesses and resistances to elemental damage. Worst case is enemies that absorb the elemental damage as healing (e.g. death damage heals ghosts) or the fact that trolls need to be killed with a fire weapon.
