From what i gather its this its not an exact increase like 5% luck = 10.5 explore rate

When you explore and it says 10 acres per turn you might get 8,9,10,11,12 etc etc

So in their forumulas for missiles and explore they have a random fact. It increase the random factor positively by 5%.

So gives u a higher chance of getting 11 acres or 12 acres per turn.

I dont have the forumula, so a mod can tell u if it actually works out to be a 5% increase in exploration rate or not.