Some ideas:

-Filofax Malden if your A5 paper is loose leaf. Card slots can be used for mini sticky notes.

-Galen leather zip portfolio if your A5 is a bound notebook. Recommendation from r/notebooks. On the pricier side but gorgeous & so enjoyable to use.

I like these 2 options specifically because of the all-around zip so nothing falls out at work. Both are leather.

-Mochithings has A5 folios with various sized organization pockets (fabric only). Similar versions on Etsy in a variety of materials.

-You mentioned you’re not using a tablet but I wouldn’t rule out looking at tablet cases. I’m pretty mobile at work & am only in my office a few times a day. Currently carrying a Caselogic tablet case with handles. Comfortably holds A5 notebook & pens, sticky notes, work keys, inhaler, & hand sanitizer. Having the handles made a big difference in the functionality. It’s essentially a zippered sleeve. Not in the materials you prefer but similar styles available on Amazon & Etsy. Mine is older/thrifted but similar to this:

https://www.amazon.com/dp/B00C8ZGK54/ref=cm_sw_r_cp_api_i_XpveFbRXD06Q6

And now I will think of it as my adult trapper keeper - thanks for the idea!