Basically, there are about 20-30 level 5 missions, half of which have gates and half of which don’t. Level 5s are kind of crazy in terms of enemy DPS and neuts so some people figured out that you can use a carrier to do the non-gated missions and it completely trivializes them. The problem is with one toon you run out of non-gated missions, so the solution is to have an alt on a separate account that has above 7.0 faction standing so he can pull missions for you. Your main must also have 7.0 faction standing.
So you get both of them in a fleet together and they share mission rewards. The reason you want faction standing and not corp or agent standing is that when you decline a mission you only take a .01 hit to your faction standing, while you take a much larger hit to corporation and agent standing. This is all predicated on good social skills, primarily Diplomacy and Connections. With these two skills and two pullers, one being your main and one being your alt, you can basically run level 5s ad nauseam. You can decline until you have -2.0 corp or agent standing, and your faction standing will be unmarred.
Level 5s also pay really well, but do so in bulk LP so cashing in is a royal pain in the ass which takes a few hours. Granted most only do it once every few weeks or a month. You can easily make more than enough isk to plex the second account though so having a faction puller isn’t difficult or costly when you have the carriers to grind l5s with.
Lastly I just want to mention that all of this is made moot by the new Glamourex boosters. Particularly the Glamourex 75. It basically makes it so you can decline missions with no standing hit and run level 5s or whatever else with one character, declining to your hearts content. So… if you want to increase your income doing level 4s try the Glamourex boosters, and then maybe consider doing your missions in low or npc null and cherry picking the easiest missions and best paying burners. Also consider getting your faction standing up so you can decline more.