For your original question, 3-5 minutes seems like a long time to push Morphine... and it is. Maybe 2 minutes would be more realistic. I know I give it a bit faster than that, and 9 times out of 10... I would only be giving 3-5mg the first round, then reassess the pain and continue on.
But you gotta follow your protocols.
Now, to expand a few things many medics have not been taught, is the priming volume in your IV sets/PRN adaptors/extention sets. Most companies print the priming volume on the sets, this is IMPORTANT.
For instance... my standard 72 inch IV set has a priming volume of 17ml. The PRN adaptor at the end of that is an additional 3ml - with an injection port in the middle of that PRN adaptor. ( my sets also have a backflow preventer, no need to pinch lines anymore ).... again... know your equipement inside and out.
If your set does not say it, measure it out. Simple enough to do.
This is where it makes you think.... So you need to give 10MG morphine, in my world, it is a carpuject 10mg/ml tube. So that 1ml will be my volume.
If I inject that into the closet port to the pt, right in the middle of my PRN adaptor with a prime of 3ml.... it would make sense that the port requires 1.5ml of fluid before the pt gets the dose.
( read that again if you need to )
So you S L O W L Y push that 10mg into the line.... guess where it is? Still in the line. The 1ml (10mg) was not enough to make it to the pt. You just spent 3-5 minutes pushing that MSO4 in the line and the pt never got it yet. Then you open the line to flush it in... ya know what? They just got that 10mg whopping fast.... head rush.. nausea.. vomiting... you know the drill.
You may as well just inject it quickly into the line, then drip it in slowly. Almost always I get a small little air bubble that was trapped in the first time use injection port.... so I use that as a guage of where my drug is in the line, and follow that bubble adjusting my drip rate to make sure it goes slow. ( little bubbles won't hurt anyone, the body does great absorbing these, just don't daisy chain 100 bubbles in.. duuhhh )
The other option is to inject it slowly with the line flowing, just make sure it does not back flow into your syringe, then that can mess up your concentration increments in the syringe.
You can always request a syringe pump, then you can get some hands free assistance... and you can spend that 3-5 minutes actually doing work.
Honestly, I have never seen anyone push MSO4 over 3-5 minutes.... its usually somewhere around 30 seconds, or they just break the dose up.. give 5... check them out... give another 5. Never have needed to diluted it either.
5mg will give great relief for a fracture pt who has never had morphine before.... on the other hand, the cancer pt with a tolerance may need 30-40mg at once.
Talk to your pt... "have you had MSO4 before?" If so... how was it?
good luck!