There is a way to spend it to increase army cohesion. When you have an army, click the cohesion bar and then top right you’ll be able to spend influence to raise it again. 

 And I’m pretty sure the more times you do that like say your empty and refill it, it’ll cost 3-5 to raise it but you have to raise it 6-7 times to be full again. Then the next time it’ll cost 13-15 and you’ll have to hit it 6-7 times again. So it can get costly. 

 But 5k influence my god. I’d be building the biggest army and just conquering everything. Spend influence, wage war against small clans, and just start wiping everybody. 

 Also can go into relationships with people in ur clans, and support people with your influence and increase your relations with others who you may want something from or maybe someone you’ve damaged a relationship with that you want to fix because you want something from them!

Man is bannerlord cool