A number of places in the chain of events that can have that kind of delay. I'll walk you through most of them. Included You can get a diagram of a typical Fire Alarm System
here. It includes the "calling the fire department" part.
Keep it, make copies for distribution. While reading the rest of this, you can use it as a reference.
Water Starts Flowing with Designed-In Alarm Delay
Almost all sprinkler systems have an anti-false alarm delay built into the waterflow switch. It's usually an air damper with a rubber diaphragm. Most of the time it's set to :45 seconds, but may vary according to what the local fire marshal says it should be. Until that :45 second delay is over, the switch won't send a signal to the fire alarm control panel.
When the rubber diaphragm in the damper dries out, almost always the delay shortens up. I've seen the delay shorten up to :08 seconds.
This delay is the time that water is allowed to flow before the waterflow alarm is sent to the fire alarm panel. But, if the alarms were sounding throughout the building for five minutes before the fire department was called, the waterflow switch delay was not the cause.
Fire Alarm Panel Sounding the Alarm
The fire alarm panel sounds the alarm, and it starts the "call-the-fire-department" signal at about the same time. Also, unless something was wrong with the fire alarm panel, the fire alarm panel sounds the alarms almost immediately after it receives the alarm from the waterflow switch.
Dialer/Communicator Contacts the Monitoring Company
The dialer/communicator can be part of the control panel, or it can be in a separate panel. The dialer/communicator starts it action almost immediately to contact the monitoring company.
The dialer/communicator is looking for an acknowledgement from the monitoring company that it received a signal. If, after a number of tries, that acknowledgement isn't received by the communicator, the communicator goes into trouble, and an amber light and local buzzer will be turned on.
The fire department doesn't want to be called by a machine, like a fire alarm panel. There are too many extraneous signals that automatic machines keep sending. The fire department only wants to hear about emergencies. For fire alarm communications, there's a go-between.
The go-between that the fire alarm panel calls is the monitoring company (usually a formal Central Station monitoring company). The procedure is that, using electronic signals, the local fire alarm panel contacts the monitoring company, who then calls the fire department that comes up on the call list for that account. They don't call 911 because there are a lot of 911 services throughout the country. Just calling the correct fire department emergency number is a lot quicker.
Most of the time, these monitoring companies are very professional, and have procedures that make sure the calls are prioritized correctly. Almost always they are on the phone with the proper fire department in less than half a minute.
A few monitoring companies aren't really the formal Central Station and don't have all those procedures. It doesn't happen very often, but I saw where one monitoring company took 15 minutes to contact the fire department (in that case as the fire marshal was looking at his watch).
I doubt the monitoring company is the delay you're concerned with, but they have call records and you can request those records to see when they received the call and when they took the action to contact the fire department.
Fire Department Dispatch
The fire department dispatch could conceivably have delayed the call, but I've never seen that.
Did Someone Else Call the Fire Department?
There is always the possibility that somewhere in the chain between the flow switch and the fire department dispatch, something didn't work correctly. If so, that needs to be checked out.
Another possibility is that the fire alarm system was never set up to call the fire department. I know of quite a few smaller systems that are that way. Someone has to normally call in if the alarms sound.
The fire department will have some sort of record of who called with an emergency. If it was a monitoring company, the call will have come in on the fire department's emergency line. If it was a private person, the call will have come in on 911 or 999, depending on the emergency number at your location.
If a private person called it in, good for them. They may have called late, but at least they called.
When The Alarm Sounds, Call the Fire Department Yourself
On the included attachment is a procedure of what to do if the alarm sounds. The idea of a separate phone call to the fire department was given to me by a fire marshal. The fire marshal was basically saying that when lives are in the balance, it's not a good idea to be too dependent on fallible technology; call the fire department with an extra phone call. Your phone call might be to 911 or 999, whatever the emergency number is at your location.
Fire departments usually don't mind getting extra phone calls from someone on site saying, "the alarms are sounding off, but I don't see or smell any smoke", or someone saying, "the alarms are sounding off, and the halls are full of smoke". Depending on what was said during the extra phone call, the fire department will enter the building two different ways.