save file list in variable or file.
FILES=$(find ...)
or
find ... > /tmp/$(USER).flist.$$
then you can remove the files after the tar, without running find twice, (which might be a heavy process or) its state may change between the first and second iteration, causing you to actually lose data.

For example: if you run the command close to midnight. the first +5 will find files just older than 5 days and the second running after midnite will add files a day older. and even if you use it in the middle of the day, the timestamp of files can cause a miss the same way.