A dry-erase playing surface and dry-erase index cards.
3x5 index cards are fine. There's a product called "the Noteboard", a foldable mat of these cards in a laminated grid, which is excellent for use as a play surface and can be cut up into individual cards if you can't find them laminated individually, but "dry-erase index cards" worked out pretty well for me there.
Players put their full five Aspects on cards facing outward from themselves. Everything that'll be moving around gets individual cards, attached Aspects get tucked under at a corner, and everything relatively static gets drawn on the mat directly.
I've had a lot of success using these tools, up to and including con games at those ten-person circular reception tables, and never had trouble reading players' Aspects even if they were seated opposite from me.
A dry-erase surface is reusable and dry-erase markers allow you to more easily make large, visible strokes, but maybe the most important feature of this setup is that it allows for the easy use of color-coding, so long as your players and the opposition all have their own color of marker to use. Just knowing who an Aspect is associated with can be a big help in -- whoop, hang on, new header.
Practical Considerations of Aspects in Play
The name of the Aspect is never the entire thing. All Aspect names stand in for a universe behind themselves that can't possibly be summed up in five pithy words. A good name will evoke a large and relevant portion of that universe behind, but the surface name is never the entirety of the Aspect.
NPC Aspects don't need to come out unless they're relevant or the players discover them. Aspects made with Create an Advantage have the entire in-person play situation already hinting at what they should mean, so you don't need a big complicated name to describe them.
This is another advantage of color-coding - when everything has its own associated color, that's some free extra context for whose Aspect it is or who made it, which should help with keeping Aspect names short and punchy.