Check around the speaker case to make sure there are no dents. Scratches are probably not a problem, but if it appears to have been dropped, the electronics inside could be damaged.
Look through the grill at the speaker cone. The cone should be clean and even with no ripples, tears or particles on it. Remember to check the horn, too. The horn helps reinforce the mid- and high frequencies that give clarity to the sound. The cones can be damaged if the speakers are connected to an over-powered amplifier.
Plug in the speaker, preferably to the system you will be using although any system will help. Listen at low volume for any humming or hissing. These should not be noticeably loud. Also check that the plugs fit snugly and securely. The Peavey 5.5P has both balanced XLR and unbalanced 1/4-inch inputs, so bring a cable of each type.
Play some music through the speaker (a recording you know well is best so you can listen carefully) and gradually raise the volume. Listen carefully for any buzzes, hisses, pops, crackles or other anomalies. These could be signs of internal damage or past overuse. Also listen for a good reproduction of the recording. No frequencies should be lower than usual or buried in the mix.
Take the speaker and test it at a band practice or speaking engagement. Push the volume to the level at which you will play or talk and listen for cracks, pops, hisses, hums and any other undesirable sounds.