The first 5 volumes are never reconstructed or saved to DICOMs. They were acquired only to allow for T1 saturation. So if the user requested 320 scans, 325 will be acquired but you will only have 320 volumes saved to DICOMs, and therefore a 320 volume NIfTI file. Therefore, you do not need to delete any volumes.
If an optical trigger was used, the offset time for the offset of the E-Prime event that paused the experiment until a trigger detected corresponds to the first slice of saved fMRI data. If you use an RF trigger, the offset of the E-Prime pause occurred 3600ms before the first saved MRI data.
Consider an EPrime output in milliseconds
Pause.OnsetTime 1000
Pause.OffsetTime 3800
red_square.OnsetTime 5000
red_square.OffsetTime 5600
blue_square.OnsetTime 9400
blue_square.OffsetTime 10000
...
If you used an optical trigger, you would subtract the pause offset time from each value when generating your events.tsv:
onset duration trial_type response_time stim_file
1.2 0.6 go 1.435 images/red_square.jpg
5.6 0.6 stop 1.739 images/blue_square.jpg
e.g. the first event occurred 1.2 seconds after the first saved slice.
If you used a RF trigger, you would subtract the pause offset time (3800ms) plus the dummy scan time (3600ms) from each value:
onset duration trial_type response_time stim_file
-2.4 0.6 go 1.435 images/red_square.jpg
2.0 0.6 stop 1.739 images/blue_square.jpg
e.g. the first event occurred while dummy scans were still being acquired, 2.4 seconds before the first saved slice.
I strongly suggest using an optical trigger. Siemens, Current Designs and PST all sell these. Or you can make one yourself. The fiber-optic trigger sends a brief pulse of light at the start of acquisition for each EPI volume (except dummy volumes). Since the signal is optical, not electric, there is complete electrical isolation between your detector and the scanner (there is no way to damage your scanner). While some vendor’s optical triggers emulate mouse or keyboard clicks, as I note in the linked page I prefer emulating a joystick button press. This will not enter the keyboard buffer and will allow you to use work on your EPrime computer when you are acquiring EPI data (e.g. you might want to set up an EPrime experiment while an EPI-based DTI scan is being acquired). In my experience RF based triggers are very finicky, and you need to make sure they only detect the scans, not the variable-duration shimming that precedes scanning.