The question is pretty simple. Multiclass characters get half their non-martial adept levels + full martial adept levels for initiator level. However, what happens when the level is odd? Do you round up or down?
Your initiator level is 5.
Every class apart from your martial adept class counts as half for your initiator level as you mentioned. But how to divide the odd numbers? Rounding it down.
Tome of Battle, pg. 39:
For example, a 7th-level crusader/5th-level swordsage has an initiator level of 9th for determining the highestlevel maneuvers he can take as a crusader. As a result, he can take 5th-level crusader maneuvers. As a swordsage, his initiator level is 8th, allowing him to take 4th-level swordsage maneuvers.
As you can see, both of the different classes in the example are odd and they are rounded down (like basically everything else on D&D 3.5) to determine each class initiator level.