If I buy the Lightroom 5 standalone download, can I put it on multiple of my computers without having to buy it again?
You may have at most two computers running the single license, where the second computer is either a laptop or a home computer. But you can only use one copy at a time:
2.4 Portable or Home Computer Use. The primary user of the Computer on which the Software is installed may install a second copy of the Software for his or her exclusive use on either a portable Computer or a Computer located at his or her home, provided the Software on the portable or home Computer is not used at the same time as the Software on the primary Computer.