not to loose quality and have a relatively compact size at the same time.
The best you'll get is probably the MXF OP1a export using the AVC-I codec.
I wouldn't throw away valuable chroma info going to 422 if you have 5K footage.
I'd find a AVC-Intra or other codec that is 444.
MPEG2 doesn't support 444
h.264 does but I'm not aware of any Premiere plugin encoder that does 444.
I think you're better off staying with the ProRes444. 1Gig isn't that big since 1Tb is less than $100 these days. Heck, 1Gig fits easy onto a usb thumb drive - so shipping it to someone is still dirt cheap.
for 5 minutes that's 10x more (5min = approx 10 x 35seconds) so you're still only looking at 10Gbytes total size.
If storage is important stay with an 444 format with some other non-ProRes/DNxHD format like h.264 (assuming you can find a 444 solution).