My party and I have been slowly building an army over the past several months of sessions with people of various cultures around the world that seek glory. Last session we defeated a large army of viking-esque warriors and (probably not the best idea but they are from my character's homeland) we recruited many of the survivors (~4500) to my army (~5000 with many more being recruited daily). The issue I am expecting to face is that the brutal and semi-xenophobic nature of the new warriors is going to clash with the variety of my existing army. Wondering if anyone has any ideas of how to address this problem over time.

History is littered with examples of polar opposites suddenly finding themselves forced to work together.  Sometimes it works, sometimes it doesn’t, often it only works briefly, but implodes.

Your best bet is to find a singular, uniting motivation. Often this is an external threat which forces the two entities to work together.  In terms of long-term unity, history has also shown that the victors going out of their way to build up the defeated helps mend wounds (see the Marshall Plan, for example).

The specifics on how you do that, however, are going to be entirely up to you and your campaign.  You will need to use the knowledge of your army, their culture, the potential threats of your campaign, what the enemy was doing invading in the first place (to see if there is something you can offer them for peace), etc. then come up with an individualized solution which works for your world.  That is not something we on the internet can really help with, for we do not know your campaign. Nor is it something we should really help with, as it would be unfair to your other players and your DM if a bunch of strangers gave you a solution (as opposed to some general “here is where to look for a solution guidance) to your campaign’s problem. 

Yeah I'm not necessarily looking for the solution I was more looking for places to get inspiration from and general advice, that's why I didn't go too much into cultural details. I think I can find a way to make this work.

Tyranny of Dragons has a fairly decent largely role played set of counsels among opposing factions in Faerun, and eventually the metallic dragons trying to get it together to create a united front against Tiamat.  That might give you some inspiration on how to gravitate from mutual interest to actual trust and alliance.  The more recent Dragonlance book might have something similar, on a bit smaller scale, but overall I didn't care for that book's adventure.

The easiest thing is to not have them actually integrate into the existing army but instead function as a separate force.  Really, you don't want to try flooding an existing army with a bunch of new recruits who aren't used to the way you do things in the first place, even if they're not semi-xenophobic against the main army.