Add a low value current sense resistor in series with the output from the 5V supply, and then measure the voltage across it to determine current. In other words, do it the same way your multimeter does (it measures current internally by looking at the voltage drop across a low value resistor.)
Later on, in 'production', you can replace the shunt resistor with a shunt. (If this is important, and current margins allow, pick a standard case size so you can put a 0ohm resistor in there later.)
If you want to bring the ends of the resistor out to a connection, use a separate pair of tracks to make a kelvin connection as directly to the pads of the resistor.
Generally test points aren't brought out to headers like that, but to little pins like this which you can clip a lead to. I'm no expert, however, in PCB design. If you have a ready made lead to connect a header to your multimeter (in voltage mode) go ahead and use a header. But if people will be clipping leads to it, clipping two test probes to a 0.1" pitch header is quite hard.
Note that what you're proposing will work, but has quite a few disadvantages:
- When measuring it adds long wires in series with the output of the psu. This will change the regulator's inductive load and may effect performance, or even cause oscillation.
- All the current has to go through that tiny little header.
- All the current has to go through a tiny little header shunt when you're not measuring.