So cute! Looks 4n.
Culture tips?
I, too, think it most likely to be 4N.
I really don't think, I'm the right guy to give optimal, cultural tips, as my growth conditions can't be described as such.
I love Sophronitis, though - and, yes, I know, they've been transfered taxonomically to Cattleya - but on my own windowsill I will persist, no matter, to keep the old name for the plants, described thus by Withner.
Optimally, most of this genus will do best in a cool greenhouse - that's not quite on, when you live in a smaller, fifth floor appartment. I try to accomodate the growth conditions the best I can:

At the moment (winter) the plants get a wee bit of coolness from the window - and I try to keep the window partly open as early in spring untill as late in the fall as possible. What I will try to optimize this year is providing better shading, when the sun is strong during spring and summer.
I grow the plants in my usual inorganic growth medium (Greenmix), that provides a nice degree of constant moisture, while at the same time, due to the waterrepellent ingredients in the mix, gives the roots sufficient "air" around them not to rot. Greenmix must never dry out completely - and you know you are using it right, when a layer of green moss forms on top of the medium. The humidity around the plants is also to some degree helped by the humidity tray.