This is the kind of situation where I’d normally caution a person to
not try to use typology as a cornerstone of their strategy. The problem is specific and personal and clearly means something to you. Typology as a lens has a tendency to flatten the dimensions of interpersonal relationships, and is too easily used to rationalize or handwave instead of accurately explain. It can really be counterproductive to rely on it too much for orienting yourself when engaging with other people.
(I use it to describe trends in interactions between certain broad “types” of people that I have observed, sometimes, but typology doesn’t play a big role in the relational decisions I make and I’ve limited its role there because I’ve seen how cartoonish things can get when people overemphasize it.)
Your knowledge of yourselves as individuals and of how you have interacted in the past should inform you. If you need more than that, it would be best to touch base with someone that knows you both and ask them for advice if possible IMO. If that's not doable either, treat him as someone you'd like to get to know better who hasn't gotten the best impression of you to date.
The common sense thing would just be to reach out in a reasonable way, maybe through an invitation to do something fun or by asking a sincere question about something he has background in. If it’s appropriate/helpful/necessary you can address whatever tension has grown between you, calmly. Then give him time and space to respond (don’t get attached to an outcome or be hard on yourself if he chooses not to meet you in the middle) and see what happens. Also, assess the part your behavior has played in the rift that’s grown between you, whatever part that may be, honestly and realistically. Commit to dialing some of it back in future interactions with your bruv.
The only things to keep in mind that may be related to type that I can think of are that a) his apparent worldly success probably has more significance for you than it does for him, it's unusual for 5s to be very anchored to that kind of thing, b) obviously if he’s a fit for 5 he won’t respond well to feeling pushed, so don’t push, c) obviously if you’re a fit for 3 you don’t like to fail, so even if things don’t work out the way you’d like, try not to construe it as a failure - if you start to see it that way I would think you might be more tempted to push, d) even if the gesture helps repair something, he may still keep you at what you perceive to be a distance because, well, 5 – distance is just part of how we cope and who we are. If you make a fair, self-aware, well-intentioned attempt at fixing what you want fixed or checking to see if things are okay between you, you’ve done your part… that’s a win in and of itself.
Incidentally I have a probably-type-3 sister who I have been estranged from. If you think you can get insight from
our little microcosm of interaction: I do think she resents me for not working as hard as she does – and it’s true, although I’m not lazy I generally am not a match for her in that way. On the flip side, I admire her because she has a kind of grit that I lack and that would be true regardless who ends up with a bigger paycheck or whatever. I also admire her natural social savvy. She is rather Machiavellian and compulsive about impression management (I'm out of step/out of touch in a way that can mess that up for her) and that’s been a source of friction between us at times. I have no plans to reach out to her currently, but it isn’t entirely for lack of regret about the state of things.
@Nissa Nissa just gave a lot of good practical relationship building/reparation advice there.