"Not enough Memory" usually means just what it says, that you don't have enough memory to perform this particular task.
The solution is to have BOTH a 64bit operating system and 8GB or more of memory. One or the other by itself will not solve the problem.
If you can't make those changes immediately, your only other choices would be to make sure that there are no other applications open when you export and/or to export from the Library Module only as that seems to work for you.
Thanks for your reply, I appreciate your feedback. I'm confused though as to why it would work in "Library" mode, and not "Develop" mode. Adobe requirements for running Lightroom do not mention the need to have a 64-bit operating system, and they say it can run with 2GB of Ram, and 2GB of free space.
Lightroom 5 Requirements:
•Intel Pentium or AMD Athlon 64 processor*
•Microsoft Windows 7 with Service Pack 1, Windows 8, or Windows 8.1
•2 GB of RAM (8 GB recommended)
•2 GB of available hard-disk space; additional free space required during installation (cannot install on removable flash storage devices)
•1024 x 768 display
•DirectX 10-capable or later video adapter
•Internet connection and registration are necessary for required software activation, membership validation, and access to online services.†
Perhaps Develop module uses more memory than Library Module, leaving less memory for exporting?
Perhaps you have heard somewhere in your travels that computers with superior hardware perform better than computers with lesser hardware?
When LR5 is launched it only loads the Library module into memory. Each LR module you open uses additional memory, which is about 200MB for the Develop module. The best you can do now is insure the maximum amount of free memory is available by closing all applications, restarting Windows, launching LR, and do not open the Develop module. You'll also need to determine how many files you can be exported before the memory limit is reached. Do your exports in batches of no more than this number of files. When each export finishes, close LR, wait a few seconds for memory to be released, relaunch LR, and export the next batch.
Best solution is as dj_paige has suggested.
Thanks! I appreciate your feedback and suggestions, and for explaining a little more about how the different modules use memory.