I want to purchase Dreamweaver CS5 for my work computer because it is the same version I have on my personal computer, and I want the two to be compatible. However, there are other Adobe CS4 programs on my work computer (InDesign, Illustrator, etc.). Will any problems arise by having Dreamweaver CS5 and other CS4 programs on the same computer? Any input is appreciated. Thanks in advance!
don't fear anything. On my computer (on the desktop too) you will find many other Adobe programs: Adobe Web Premium CS4, and different versions of DW (starting from Dreamweaver 4 about Adobe Dreamweaver CS3 till newest, aso.) which I use to compare and have a closer look at some websites.
Are you intending to purchase a standalone version of Dreamweaver CS5?
Your work computer has probably got a CS4 Creative Suite installed (Design Premium CS4?).
You won't be able to upgrade Dreamweaver CS4 (from the Suite) on your work computer to standalone Dreamweaver CS5. It's not a valid upgrade path.
Tip: CS6 is due to be released very soon.
Although free upgrades from CS5 (purchased after 26 March 2012) are available, there is some paperwork involved. In your position, I personally prefer to wait until CS6 ships - unless CS5 is really the version you want, of course.