I would interpret this as 7, RAW. (Backgrounds and Familiars don't seem to be in the Compendium, and I'm not on Windows so I can't check the CB, so I'm assuming the wording in the OP is what's in the books.)
If you have fire resistance from multiple sources, you keep the highest resistance; they don't stack. (Hmm, I wanted to quote chapter and verse on this, but I can find where it's spelled out explicitly. Do I have that right?)
So Akunal gives you two options: you gain resist fire 2, or your existing resist fire increases by 2. It doesn't specify when each option takes effect (although obviously the second requires an existing resist fire.) For instance, if it said, "if you already have resist fire, it increases by 2 instead", then it would be spelled out exactly when you must take the increase. But as written, I think it could reasonably read as player's choice: you can choose to gain 2 fire resistance, or you can choose to increase your existing fire resistance by 2. (If you have existing fire resistance, in most cases it would be stupid to take option 1. However, you might interpret it to say that you must make the same choice for ALL resistances, in which case both options could be valuable: if you already have fire resist > 2 but not cold or thunder resist, you could choose to take resist 2 cold and thunder, but no additional fire resist, or you could choose to increase your fire resist but forego the cold and thunder resist.)
Book Imp does NOT use the word "or". So I would say that if you already have resist fire 2, both clauses come into effect: you gain resist fire 5, and then since you already had a resistance you add 2 to get 7. (This can be considered a bonus the imp gives to characters who already have some fire affiliation.) If you already had resist fire 10, you would gain resist fire 5 (which is useless since you already have 10) and then add 2 to get 12.
So, the player gets to choose between:
Akunal grants resist 2: total resist fire is 7 from Book Imp.
Akunal raises existing resistance: total resist fire is 5 from Book Imp (since Akunal does not grant basic fire resistance) +2 from Akunal (since the character has existing fire resistance from Book Imp) for total 7.