What you describe is normal and necessary. Do not worry about it.
When a fan starts up from a stopped condition, it takes more voltage than to just keep the fan running after it is already running. How much? Certainly more than half the maximum voltage. So, what BIOS designers have put into place is a sequence like this:
1. When power is turned on to start the boot process, by default all fan headers send full voltage to their fans, so all fans are guaranteed to start up and reach full speed.
2. A whole bunch of other work needs to be done for the POST processes to be completed and the boot process to begin, so this takes a few seconds.
3. As the boot process (using the boot drive) is beginning, the temperature measurement systems in the BIOS software fan controllers start to work, receiving temperature readings from the sensors in the CPU and mobo. At about the same time the fan failure monitoring systems start to get reliable speed signals from the fans to verify that they are working properly. Once the temperature reading systems have a reliable value the fan control systems can start their normal function. Don't forget, these systems are TEMPERATURE control systems - their purpose is to keep the Temperature as measured at the two sensors at target values, and they do this by changing the fan speeds. So with a reliable reading of each temperature, the control circuits can start to alter fan speeds to achieve that.
All that has to get done before the fans can slow down. 5 seconds? Seems OK to me.