That should be an ok load assuming the stats courses come easy to you and the history isn't an overwhelming amount of reading. Real analysis will probably require a lot of time outside class doing exercises and proofs. Numerical analysis will most likely have computer lab assignments pretty regularly. I always stuck to a schedule of 2 technical (math/science/computer) classes, 1 humanity/language, 1 music theory/history, and then my lessons and ensembles, which was usually a 13-14 credit load, but I was a MUSIC MAJOR (where a 1 credit lesson required 2-3 hours of practice each day, and a 1 credit ensemble = 3x 4 hour rehearsals, plus I worked 20 hours a week at my part-time job. If you've taken 4 math/stats/computer courses before in a semester, plus one gen-ed and handled it well considering all the other stuff that may be in your schedule, then there's no reason this next semester will give you any trouble.
Most courses in numerical analysis require you've had calc 2, differential equations, linear algebra, and know a little something about programming (any language). The goal is to learn how to model problems and arrive at numerical solutions using a computer (sometimes by hand + basic desk calculator just for "having done it" ). An assignment we had early in the semester was to use excel to solve definite integrals, and some differential equations. This was over a decade ago, so maybe classes now don't do exercises like that anymore with , but eh whatever, should give you a small idea of what you'll be doing / that it is [was] a more computer focused course.
Real Analysis usually requires that you've had the whole calc sequence, linear algebra, and some sort of intro to proofs / abstract math course. Some real analysis courses could actually be taught along with calculus if done correctly, but that's probably not an issue, nor is this a thread to discuss the merits of that line of pedagogy.
Assuming you have those, you should be fine with both of them. You're not really going to be learning stuff in one that requires exact skills from the other one. Considering it's probably your first abstract course, real analysis will most likely be more work unless the numerical analysis class requires absolutely insane projects.
I would make sure to read ahead on the real analysis course so you're not going into lecture blind and just taking notes. If the lecture is a refresher, you can take more illuminating notes. Harvey Mudd put up full lectures on youtube that are pretty good, probably not the most rigorous, but certainly will help if you need some extra lecture time on certain topics during your first semester of analysis.
Good luck.
