You always need the latest game update to play online.
Sometimes you need the latest firmware, and sometimes you don't: there was a time when 5.3.2, 5.4.0 and 5.5.0 were all allowed online, and then one day, Nintendo changed their mind about 5.3.2 and 5.4.0. Right now, 5.5.0 and 5.5.1 are the...