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Please remember that Deadly Aim is not applicable to touch attacks...
Deadly Aim (Combat)
Prerequisites: Dex 13, base attack bonus +1.
Benefit: You can choose... The bonus damage does not apply to touch attacks or effects that do not deal hit point damage.
This takes 4 off of your damage for every shot. It does not affect the +7 to hit, as that math was off by 2 anyway.
Deadly Aim explicitly works fine with firearms.
Early Firearms: When firing an early firearm, the attack resolves against the target’s touch AC when the target is within the first range increment of the weapon, but this type of attack is not considered a touch attack for the purposes of feats and abilities such as Deadly Aim. At higher range increments, the attack resolves normally, including taking the normal cumulative –2 penalty for each full range increment. Unlike other projectile weapons, early firearms have a maximum range of five range increments.
Advanced Firearms: Advanced firearms resolve their attacks against touch AC when the target is within the first five range increments, but this type of attack is not considered a touch attack for the purposes of feats such as Deadly Aim. At higher range increments, the attack resolves normally, including taking the normal cumulative –2 penalty for each full-range increment. Advanced firearms have a maximum range of 10 range increments.
Double barreled firearms don't work that way anymore. You can only fire both barrels as one attack when using the standard attack action.
At 5th level, you'd get three attacks--one from the primary, one from the off-hand, and one extra from Rapid Shot. Having two barrels per weapon wouldn't even enter into it. You'd need haste or something similar to get a fourth attack.