OS version and TR refresh level upgrade question

We are currently at 7.2 TR5.

I am not the sys admin here. (just an RPG developer :-)

To the point. . In an effort to keep things close to current here I'd
like to direct the powers-that-be to either upgrade the OS to 7.3 or get
our tech refresh more current.
(I need to enter a help desk ticket to spur this)

I doubt I can push an OS upgrade to 7.3 thru at the moment but, i can push
to do an TR upgrade.

I see the current TR for 7.2 is TR7 (and we are at TR5).

Should i request we go from TR5 to TR6 or should i request we go from TR5
to TR7 ??
(i don't even know if you can jump from 5 to 7 for TR's)

Thanks for any help, thoughts or general direction.

John
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