I'm planning on taking about 5,000 product images and I need to catalog them. I am aware of Lightroom, but is it used on a large scale? Is there another program that larger companies or organizations use?
The biggest challenge to Lightroom is concurrency, not the size of the catalog, which can support up to one million images. Concurrency is not supported by Lightroom at all. While professional asset management software is designed for multiple clients all accessing the same database at the same time.
For that type of environment, look at DAM software from Extensis. There must be other such software, but the ones I knew appear discontinued.
The companies like Target and Macys most probably use Enterprise level digital asset management (DAM) systems with pricing started from $100k, complex deployment, and with some level of learning curve.
Are you really need such system for 5k assets?
LR can handle your image archive library easily, but as Itai said: concurrency is the biggest challenge of Lightroom.
Another big challenge of Lightroom (and any other standalone photo organizer) is the potential risk of damaging your catalog located on shared locations. Because a remote computer might be disconnected for some reason during catalog updating and this leads to completely damaging and losing of your catalog data and annotations.
Unfortunately StackExchange rules don't allow me to offer you a multi-user photo management software at an affordable price that can fit your requirements. Because this might be treated as an advertizement of a company where I work ;)
I happen to know that there is a product called FotoStation (www.fotoware.com) that is used as an image management, search and retrieval system for newspapers and that kind of thing. Doubtless there are numerous others. But, truth be told, your five thousand images are nothing, nothing at all, compared to the massive amounts that such systems are designed to handle. Lightroom will easily be able to do it.
I have approximately 80,000 images in my Lightroom with multiple tags, smart sets and other meta information (camera, lens info, etc). No issues with being slow or unresponsive.