Newbie Question: What do speeds mean on chains?
A bike with a 5 cog cassette requires a 3/32" 5 speed chain which has also been referred to as the "10 speed chain". This is different to a modern 10 speed chain though as below.

In rrecent times speeds refer to the number of cogs that make up the rear cassette. Outside of big box stores gearing is generally specified as YxZ. So in a department store you may see a bike advertised as having 21, 24, 27, 20 or 11 speeds whereas in a bike store it would be sold as 3x7, 3x8, 3x9, 2x10 or 1x11 (right up to 1x12 which strangely is currently referred to just as Eagle!)

The reasoning behind specific chains for different speeds is as they have increased the number of gears available on a bike they have maintained the same freehub width over the last 4 iterations. 8, 9, 10 and some 11 speed cassettes all work on the same width hub. This has been achieved by spacing the cogs closer together and producing narrower chains.

There is generally tolerance in a chain to go up/down 1 speed without issue. Ie. an 11 speed chain can be used on a 10 speed cassette.