Hi anton. I've never heard of a 5khz variable resistor, but I have heard of a variable resistor. I assume that you're using the variable resistor to adjust the output up or down 5 khz.
Simply connect the scope to the output of the 555. Pin 3, and you will see the 38khz signal. A regular IR LED connected straight to pin 3 will easily cover 10 feet as long as there is not too much light on the detector.
What kind of detector are you using? Maybe the reason that you're not getting 10 feet is because your detetor is not good enough.