Daryl, did it have it's initial "break in" service (Rocket is at 500 miles, I have no idea what it is on the Tiger), if it has I'd just go for it.
Ooooops, sorry about that Daryl, must be getting old...I blew right by where you mentioned that you already had 5,400 miles on the Tiger. I would still go for it as even if it comes into the shop with 6,500 miles or so on it I think that Dink will only say "it's a Triumph no big deal it can handle it".
Dennis
33 dtg KAF
38 dtg Dubai
39 dtg Home
60 dtg Ray's