I am planning on using multiple strips of LEDs to light up a 2 ft x 2 ft x 2 ft light booth for taking pictures of small items. LED output is Cool White 6500k. Digital camera is low cost 5 megapixel HP. Are these lights and camera compatible?
In the most basic sense, yes. The colour temperature of the LEDs is well within the range of normal daylight, and just about any camera can cope with that.
The problem is that it's highly unlikely that the LEDs you are planning to use have a good colour rendering index (CRI). All of the consumer LEDs I have seen have a CRI in the low 80s at best. That means that there are substantial portions of the spectrum that are missing and/or over-emphasized, and you won't be able to fix the colour problems in your pictures by adjusting either the colour temperature or tint settings for the photos. The light isn't there, so the data aren't recorded. There are LEDs with reasonably good CRIs (you need something in the 90s at least), but they tend to be painfully expensive.
If possible, fluorescent or incandescent lighting would be better from a bang-for-the-buck point of view. Incandescent lighting is great, but there can be some significant heat problems, especially in a confined space. (Remember the Easy-Bake oven?) Fluorescents are bulky and a bit more expensive, but you can usually find bulbs with good-enough colour rendition at something approaching reasonable prices.
6500K is roughly equivalent to outdoor, overcast, conditions. So, if the version of camera you have (you didn't specify which camera and HP has a few 5mp cameras) supports an option such as shade or overcast, that is probably what you want. Better yet, if it lets you specify the temperature to use, via custom white balance, do that.
HP does make the camera manuals available online. Just go to Google and type in something like "HP Photosmart E327 camera manual" and you'll get an immediate result. By the way, if that's the one you have... http://h10032.www1.hp.com/ctg/Manual/c00599504.pdf (see Page 39 for white balance settings).
I work as an assistant and also do my own photography. We use an LED video light much like this one
It works great, has a dimmer on the back so you can adjust how much light you want. That might be the problem with your LEDs, being unable to adjust the brightness. I highly recommend getting a video light, they're not that expensive. They also come with filters to put on the front of them which allow you to make the light more yellow or blue as needed.
I would NOT use LED lighting if colors needed to look "real". You can find a white ballance easily enough by doing test scene with a known white object, but that doesn't fix all the in-between colors. The problem with LED lighting is the the light power is concentrated in a few relatively narrow spectral lines, not spread out like black-body radiation.
Take a look at a collection of colored objects under "white" LED lighting and sunlight. The colors will look quite different relative to each other, even after your visual systems ballances for white.
If it just has to look plausible such that there doesn't appear to be any particular color cast and nobody knows the exact color of things you are photographing anyway, then it doesn't matter. If your object contain a logo or something people are familiar with the color of, then LED lighting is not a good idea.