Make sure that the material you use to cover your paper with when making the test strip is entirely opaque. Or some light will shine through and fog the paper underneath.
Also, instead of doing 5 second increments, I recommend using the values on the f/stop ring on your camera lens. 32s, 22s, 16s, 11s, 8s, 5.6s, and 4s. You go backwards like that, so that the first strip is 32 seconds, next is 22 seconds, etc. It gives you one full stop between strips and gives you a better idea of what different levels of exposure will do in your final print.
Good luck. Keep posting back here with your results.