Well first of all, motivation is a bad word to use to describe what the enneagram does. I used it before, but animegai said it best: it's the lens through which we see the world in. All 9 types' "motivations" can be experienced by everyone, and I'd be surprised if no one experienced more than one (and even more than 3) of those "motivations" in their lifetime. As a 6, I've had a desire to be right/perfect in certain situations, to be loved, to be successful, to be unique, etc., but my energy in all of these situations stemmed from feelings of being insecure and unsure of myself - the very essence of a 6. When you talk about your friend's motivations, what exactly do you mean?
Secondly, the way tritypes work is that when your primary core fixation doesn't work in a situation, you supposedly jump to your secondary core fixation and try to use that to fix the problem. If that doesn't work, then you finally jump to your third fixation to solve the situation. Contrary to how many people view the tritypes, it isn't just your top fixation from each triad, but rather, how you act when you get stressed out. If you notice above, David468 is one of the co-founders of the tritype and if you see his videos, you won't even see a trace of 8 in him. I remember a member of this site (I think it was Elfboy) saying that s/he asked David about why he was a 468 and not a 469, which would be more apt for him, and him replying that the 8 in his tritype only comes out when he is very stressed out. As you can tell, this obviously isn't verbatim, but this was what was essentially said (from what I remember).
Now, where I'm going with this is that it's impossible for your friend to display both fixations (if that is what you meant) unless he was a very high strung individual who couldn't relax in any moment. It might seem like he's a 1 and 5 because both are in the competency triad, but otherwise, both of you may probably not be typing him correctly. It could also be that both of you are just analyzing the motivations, such as 1's having a desire for perfection and a 5 wanting to be competent, which are motivations anyone could simultaneously have, instead of thinking about his fixation.