The short answer is you do not appear to have much in the way of damages. You did not say that you suffered greater physical injury because of the 5 minute delay, so 5 minutes of emotional distress is not worth much. The case would also likely fail because normally for an emotional dilstress claim there must be some physcial injury, to reduce the number of phony claims. Also, you knew for months that the phone could not be used to make 911 calls so you were partly at fault.

No attorney would take your case.

911 calls use the same software and hardware as other calls. If you're in an area with poor signal quality, that quality will be reflected in 911 calls just as it is in other calls.

As Mr. Shers said, even if the cell company did have a legal duty to make your 911 calls go through reliably (which I doubt), to win a lawsuit you would have to prove that you suffered a significantly greater harm than you would have suffered had the call gone through correctly the first time. You have offered no reason to believe this happened, though obviously you haven't given us all the facts.

FCC regulations require the carriers to meet certain performance standards. Those standards do not differentiate between what numbers you call, and do not apply to any particular call. Those standards also allow for legitmate service interruptions. Even if there was a violation of the standards, it would be a regulatory penalty, not a private right of action. What is really fascinating about your question, though, is that you were advised that cell service was interrupted in your area "a few months ago" but you relied on your cell phone for a 911 call anyway? And then you want to sue about it? I bet you're one of those people who complains about all the stupid lawuits too, aren't you? Pathetic.