I'll assume you are familiar with the risks associated with boosting the current in your light, and just tell you how to do it.
Light output is approximately proportional to current. So to get 5/4 as much light, you need 5/4 as much current. In truth, because lumens/amp drops as current increases, to actually get 5K, you need a little more current than that.
Since current is inversely proportional to the sense resistor, you need 4/5 as much resistance. You could replace the resistor with a lower value one, or add one in parallel (solder it right on top of the old one). I'll skip the math and tell you the parallel resistor needs to be 4 times the value of the original one.
There are a number of ways to measure the current.
1. Break into the circuit and install an ammeter in series with the LED. If you have good regulation, this probably won't change the current much if at all. If the regulation is poor (like a direct-drive or resistor-limited setup, the additional resistance of the meter may substantially affect the current. A clamp-on type ammeter would have less impact on the circuit, but most only read AC. Ones that read DC are not cheap.
2. Measure the battery current and the battery and LED voltages. Power in equals power out times efficiency. You'd have to estimate the driver efficiency.
3. Measure the voltage on the sense resistor and use Ohm's law. I = V/R.
Because there is probably substantial AC component to the current both at the battery and at the LED, different meters may give slightly or even drasticly different results. This is because some will give you an RMS reading, some will give an average reading, and some will be in between. Because the LED is not a resistive load, but is closer to a fixed voltage, you want something close to the average current, not the RMS.
The difference between RMS and average can be zero, or can be quite substantial. For a fixed value with no variation, RMS and average are the same thing. For a square wave with 50% duty cycle, the RMS value is 40% higher than the average, and for a 10% duty cycle, RMS is more than 3 times the average! The input current on a buck-type regulator can be fairly close to a square wave.
Fortunately, I think most cheap meters will give you an average reading, not RMS. It would be wise to be cautious, however.