I'm somewhat new to this so forgive me if I use the incorrect lingo.

I have a Specialized Allez with two "chain rings" up front and a rear cassette with 7 or so gears. I've noticed some slipping between the 3rd and 5th gears. I'll get a clicking sound and, at times, the gear will shift on its own.

I'm assuming this is a rear derailleur issue. Is this something that can be fixed via an adjustment or is this something that would require a replacement of the derailler?

Thanks in advance.
ty

From your description it sounds like a simple gear adjustment.

It sounds like an adjustment, most likely of the threaded fitting where the housing ends on the RD. Turning this in either direction effectively lengthens or shortens the cable fine tuning the position - trim - of the derailleur in each gear (lever click).

Hang the bike with the rear wheel off the ground and turn the adjuster one full turn outward. That should make the RD shift to larger sprockets more effectively and to smaller ones more sluggishly. If you turn it inward the opposite happens. Your goal is to find the adjustment with the best balance between up and down shifting, which should solve your problem.

There are other possibilities including chain/cassette wear, cable friction, mis-aligned hanger or a problem in the lever whereby it doesn't stay clicked in position properly. Start with the basic adjustment, and if that doesn't solve your problem you can move on from there. There are a number of good guides on derailleur adjustment available on the internet including some videos which you'll find to be very helpful.

First thing I would do is lubricate the derailleur and the shift cable within it's housing. The derailleur is probably being restricted by friction somewhere in the system. When the friction gives way, it shifts. Had a similar problem recently and a few drops of oil did the trick.