Bottom bracket calculations

I have a bike with a Shimano bottom bracket fitted; its label says:

BB-UN54 [part number]
68 [bottom bracket shell width]
BC1.37 x 24[what do these mean?]
LL113 [113 is the total spindle length, what does LL mean?]

It's just about OK on the bike, but the chainwheels (a Sunrace R90 Road Double Chainwheel - 50/34T FCR96) are further out than is ideal. They could easily come in 5-8 mm. So, I'd like to find a bottom bracket that fits better.

What specifications should I be looking for?

After a lot more puzzling and searching, I think I am able to answer my own questions: BC1.37 x 24 is just the specification of the thread, and most 68mm bottom brackets conform to that.

So I should be looking for a 103mm spindle width bottom bracket, and it seems simple enough.

yes, just make sure there is 5+mm free space between the bottom bracket cup/flange/sleeve and the crank arm now.

So you have some space to remove...

make sure there is 5+mm free space between the bottom bracket cup/flange/sleeve and the crank arm now

I don't follow that - as long as nothing fouls anything else, isn't that enough? Why is there a need for an extra 5mm between the cup of the bottom bracket and the crank arm?

You are going to install a 5mm shorter bb each side (113 -> 103mm). To do that make sure you have 5mm free each side now with the longer 113 mm bb. So there is space to give for the shorter BB (before you buy....)