Your images are NEVER stored in Lightroom. They are on your hard disk somewhere, in the location your put them (or asked LR to put them)
Upgrading doesn't harm your images in any way.
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Adding to what dj said, when you install LR5, it will automatically update your LR3 catalog to the newer LR5 format. It's all very easy, automatic and quick. The install process will leave a copy of your LR3 catalog, but it's always a good idea to make a backup of your catalog before upgrading.
Once you determine that LR5 is working correctly, you can uninstall LR3. The uninstall process will not touch LR5 and it certainly will not ever touch your image files.
You should be aware that some users have experienced issues when upgrading previous version LR catalogs to LR5.2. I had the following issues when converting my LR4.4.1 catalog to LR5.2. I did not use LR5.0 previously and upgraded direct from 4.4.1 to 5.2.
Spot Removal Clone/Heal Spots lose Feathering
'Constrain Crop' box becomes unchecked
I suggest holding onto your LR3 catalog and previews and leave LR3 installed for verification should you have issues. Both LR3 and LR5 can be installed and used without conflict. Workarounds are offered at the above links. Adobe is also working on a solution, which will probably be in the next update release (5.3). You could choose to wait rather do this manually. Just a heads-up in case you are affected.