I've just redone most of the engineers in my second account. This is what I discovered by trials and with help from reading the forum:
If you've only just started with engineers, do the G1 grinding. Just take-off and land nearby, then spend an hour blasting everything on the radar and picking up every fragment. Use all the fragments to do G1 upgrades, which will take you to about G3.5, then go prospecting for another hour. That should unlock G5. That makes about 3 hours to unlock level 5 with any engineer - maybe 4 hours. Then, see what you need for the G5 mod you want, then go and get the stuff.
I only counted G1 mods for G1 and G2, which were 3 and 12. Assuming that it progresses at a fact of 4, you'd need 3 to unlock G2, 15 for G3, 63 for G4 and 255 for G5. Maybe that makes sense because in binary it would be 11, 1111, 111111, 11111111, so 255 fragments to unlock G5 - maybe!
If you've been around for a while and have loads of engineers materials of every type, then doing three of each grade by travelling to get the commodities might be quicker. You need commodities for any mods above G1. It'll take at least half an hour to go and get them. The other materials are readily available, but if you don't have them, it'll take you probably at least a couple of hours to figure out how to get them and then to actually get them while at the mercy of RNG. The G1 method is at least predictable and reliable.