Many people have issues with LT05 capacities. You mention that your tape drive is 1.5TB native. Does that mean that it's circa 3TB with compression?? What model of LT05 is it exactly? Is hardware compression enabled on it?
Also, what is your backup utility? Are you using tar or cpio or some backup suite? With Unix commands you can normally set the tape capacity and, if you do that, the number of bytes backed up is "counted" as the tape is written and the command calls for a new volume when that number of bytes is reached. It has nothing to do with hitting the actual end-of-tape or anything like that. With some backup suites the tape capacity is often set in a configuration file somewhere.
As other respondees have said, please post more information of your configuration.
Meantime, search for "LT05 compression" on the web.
In this example the discussion covers not getting the 1.5TB capacity even with compression switched off (ie, native) and reformatting tapes to resolve.
LTO5 Tape is not using the complete capacity of 1,5TB (uncompressed) + Compression not working | Symantec Connect Community
Hope that helps. Please post your progress or lack of progress.