I was able to install, and run, Premiere CS5 on a laptop with a single 5400 RPM drive and 4GGB of RAM.
I use a second 7200 rpm external drive connected by eSATA for media, though.
CS5 apps won't crash if you have a 5400RPM drive. You'll simply not have the performance you desire, or remotely expect, from a 5400RPM drive. Hard drives are cheap, do yourself a favor, and change it. PremierePro works better if you have at least 3 disks to share in the workload. (Actually, the more the better, depending on your worklow). You can keep the 5400RPM drive as your system disk if you want. Or even as a backup drive. But at a minimum, the media drive has to be at least 7200RPM. Also, the more cache, the better. Get one with at least 32MB cache. 64 is better.
If you can, and budget allows, get more RAM! 4GB is too little.
Frederic is quite correct - when I increased the RAM in my laptop to the max allowed of 8GB, performance was much smoother.
Replacing the system hard drive with a Seagate Momentus XT hybrid 7200 rpm produced a further, but smaller improvement.