Suppose that my investigator currently has a fight of 4, and a Rifle (Combat +5). Is the number of dice I get to roll during combat limited by the in-box equipment (5), or can I roll 9 dice (5 dice + 4 dice)?
Roll as many dice as you need to (nine, in your case). The relevant bit in the rules, I suppose, is:
When making a skill check, a player always rolls a number of dice equal to his investigator’s value in the appropriate skill.
There's also an example, under Weapon and Skill Limits, saying:
... He then accounts for the Star Spawn’s combat rating (–3), leaving him with 13 dice with which to roll 3 successes (as the Star Spawn’s toughness is 3)
There are so many things that wouldn't make sense if you were limited to five dice. There are investigators with a skill that goes up to 6, items like the Tommy Gun that give +6 to something. And there's the bit where skill checks requiring 3 successes would be pretty much impossible, and even two would be hard. Combat should often involve more than five dice, and it's quite possible to get yourself up past ten dice - I think they just figured it wasn't really feasible to give you enough dice for any possible situation.