The test you can perform on a periodic basis that will prove that your circuit survives up to 5A could be done in the following way.
Remove the actual fuse from the fuse holder in the product to be tested.
Replace the fuse with a two wire connections that go to a special test fixture. This could be a connection device shaped like a fuse that has the two wires soldered to its ends and then plugs into the fuse holder.
The special test fixture is a thing that you would build that can sense the current through the two wires. The two wires pass through a small valued current sense resistor and a pair of relay contacts that are normally closed. When the test fixture senses current at 5A it opens the relay and latches into that state until some button is pressed to ready the test fixture for the next test.
Another part of the test fixture is designed in the proper way (specific to your product) that either injects current into or loads some part of your circuit in a linear manner from 0A up to a maximum of say MAX-A. For example, if your product circuit is designed as a voltage converter to supply a load of up to 5A at output voltage of 12V the test fixture could be designed as an active current sink load that is controlled to sink from 0 to MAX-A in a ramped manner.
Power up the product under test.
Activate the test fixture to start the ramp up of the current from 0 to MAX-A.
Check that the test fixture sensed the current at 5A and latched the relay open.
Turn off the power to the product under test and remove the connections from the test fixture and replace the fuse.
Check that there are no burned components in the product under test.
Perform the normal functional test on the product to assure that it still works correctly.
That should give you the idea of the test flow and the testing equipment that you need to build. It is clearly product specific to work out how the 0 to MAX-A current device gets designed and attached to the circuit.
You may decide to change the 5A test current level to a value that is 20% or 40% higher so that you provide some test margin to assure that the circuit in your product is fully robust all the way up to and over the 5A spec limit.