Is your laptop Mac or Windows?
Did you download the Mac or Windows installer to your laptop?
I have a Mac and a Windows laptop. I purchased a perpetual licence from Adobe and downloaded LR to my mac and installed it using the licence key. A few days later on the Laptop Iaccessed my account on the Adobe Site, found the purchase order with the link and licence code and downloaded it to the laptop and again installed it using the same key. It worked fine.
It sounds like if you have followed a similar path your key needs resetting maybe ? Have you tried contacting Adobe customer service?
Are you sure that license key is for LR5 and not for LR4? Did you upgrade to LR5 from LR4? Please see my last post to Trying to reinstall Lightroom 5 on my new hard drive and the serial number won't work.
"I purchased Lightroom 5 a short time ago and now would like to be able to load it to my Laptop. How do I do this without having to go through the purchase option again? I still have the license key number but it is read as invalid when trying to initiate the software after downloading it to my Laptop."
Its possible that you downloaded the Lightroom Creative Cloud version the second time arround. The Lightroom Key cannot activate that version. Uninstall from your laptop and then download the latest version from the link below, install and your key should work fine.
Was able to get help from the "Chat" window later in the day. They solved the problem by checking my license key and providing software to download to the 2nd computer. Thanks to everyone for the time taken to read and respond to my initial question. Problem solved!