So what you'd have is a Reputation with each race, and your selected race would get a bonus while other races would recveive a lesse bonus or a penalty. For example:
Orc Reputations
Orc: +30
Lizard: +15
Human: 0
Elf: -15
Dwarf: -30
Not entirely accurate, but it gives you an idea. I think this would be the easiest way without writing 5 separate stories.
with this i would more like go with
ReputationsOrc: +20
Lizard: +15
Human: -5
Elf: -10
Dwarf: -10