Well, these are five terms that can be picked out of the dictionary, but I believe require a little understanding of Japanese "thinking / mentality".
Basically all terms point into the same direction, making the reader wonder about the necessity to use so many different terms where one word should be enough.
There has been a comment about the English translation, so I won't refer to that and try to give not a translation into German, but an impression of what these terms mean to the Japanese.
means: Ordnung, aufraeumen
yet, this refers to the order in ones own house, around one's own work space in a rather general sense.
means: also Ordnung, geordnet
but here the meaning includes rather one's work space, where things should be put into an "organized system": wrenches here, drivers there etc.. Thus "ordentlich aufgeraeumt" would mean, you could work on your job efficiently, without having to look for your tools: they are always where they should be.
means also "Ordnung, aufgegeraeumt"
but here includes the idea also "sauber". Thus, you could for example have a workplace in "seiton" order but with an oily wrench. This does not happen in a "seiso" type "aufgeraeumt" place.
means: "rein, sauber, hygienisch"
an "ordered workplace" is not necessarily "sauber" or "hygienisch". Yet, the Japanese are very fond of the idea "clean = sauber", even if this does not apply to their world view as a whole, but rather to the little space (living or working) assigned to each person. Thus, "seiketsu" means here "den eigenen Bereich sauber und (hygienisch) rein (in a very broad sense including theological concepts) halten". Not just sweeping the floor!
this is rather difficult to put into English or German, because these languages lack the concept Japanese associate with this term. Simplified it could mean "zusammen", "beisammen halten", which could refer to things, like keeping certain types of tools together, but I believe, it rather refers to people! Keep together = "zusammenhalten", "Solidaritaet" (this is not a very good equivalent), "zusammenarbeiten" in the sense ot "stick together to get the job done". A related word refers to the life spend together by a married couple.
I am not sure my explanation will be of any help, but hope they are giving some clues. Of course, the final decision of the words to be used also depend on the type of context and intended meaning. A term found in the dictionary may not necessarily fit the requirements.
Best wishes from currently very cold Japan