I've taken most of the Engineers (the ones with the upgrades I want anyway) to level 5 multiple times each. The absolute easiest (fastest, in terms of while at the engineers' base) is to collect things for the level 3/4 upgrades (including commodities).
Three of each will get you to the next tier.
That being said, I want specific side effect bonuses, so I use the favor, which in turn means I need to re-do the level 4-5 steps...
It's a pain, yes, but, I found it you take the little bit of prep time collecting things, it's not so bad. You can do it all in one visit. As an example, I visted Sarge for the first time, sold some data/etc, then got him to level 5, then upgraded 4 cannons and favored high yield shell on each. Which translated into 12 G3 and G4 upgrades to regain G5. This is how *I* do things, which other may think is daft, but it beats making multiple trips. I had all the required materials/commodities for all the upgrades when I went there the first time. If/when I decide to get another round of upgraded cannons, I'll do it again. Same applies to Broo/Todd weapon upgrades.
I have less patience re-rolling for a specific secondary effect, so I just "buy" them via favor. The equipment storage/transfer thing helps greatly. I use an Asp for the lower level equipment, and an Anaconda for the bigger stuff, since they have the biggest jump range (upgraded).