Q: Can I upgrade straight from 10.5.8 to Mavericks using a USB install drive?

You can not go directly from Leopard (10.5) to Mavericks (10.9)

Check if you computer is supported http://support.apple.com/kb/HT5842?viewlocale=en_US&locale=en_US

If you have a MacBook, and not a MacBook Pro, you must have at least a MacBook5,1 for Mavericks to install.

If you have a full install built on the flash drive, you can install on a clean partition, which is called a clean install, but you will have to be sure your MacBook is compatible.

Yes, Mavericks can be installed on a clean drive/partition without the requirement to have Snow Leopard installed on there.  Mavericks can now build itself without the requirement to modify/update an existing Mac OS X.

If your copy of Mavericks was downloaded with your own Apple ID from the app store, then it should work; however, if it was not (downloaded with a different Apple ID), then your Mavericks install will not allow you to update apps nor much else at the app store with your Apple ID since they won't match. At least that is how I understand the complicated SLA requirements to work (I may be wrong of course).

(superceded by babowa's comment)