How long will it take to backup a full 946.05 GB from my iMac to 5TB My Passport for Mac external drive

Transferring that 1TB of data to your external hdd could easily take 4-6 hours on that Mac. If the external drive is an SSD, then maybe something less. Either way, it'll be an exercise in patience.

The problem with answering your question is there're just too many variables to make an intelligent guess, i.e. very close time approximation.

For one thing, transfer speeds are not constant and will vary as the process runs. What are the read/write specs of the two drives? The overall transfer rate will be controlled by the slowest component and I'd guess that will be your HDD. If it get 150 to 200 MBps you're lucky, whereas our Mac internal read/write at over 2,000 MBps. I think MBps, regardless you see the relative differeence.

My answer, a long time ... hours.

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I'm currently cloning an 856 GB external SSD to another external SSD and am getting the rate of 6.42 GB/minuet. So I would guess at that rate it would take you about 7 ½ hours. However, I have USB 3.1 speeds which are probably faster than what your machine has.

If you use Apple's Time Machine it can do the back up in the back ground and still let you use the computer in the meantime.

Yes, the info will still be on the original computer. However, after Time Machine does it's initial back-up you can go in a delete whatever it is you want deleted from the HD on the original machine or... you can reset the original computer to factory original condition (after disconnecting the back-up drive to perhaps use with a new computer) with Apple's recommendations "What to do before you sell, give away, or trade in your Mac - Apple Support".