Honestly your set of five at least for me depends on what I'm doing. For example if there's a fight where there's alot of aoe healing going down and the heals need every bit of help they can get, ie ex primals and turn 6 and turn 9 for example Mantra might go on my bar. For a fight where I'm not in a position to mantra or there's not alot of aoe healing, so for example twintania, I'll swap it out for second wind. Thats just one of my hypothetical.

Anyway good cross class skills are

Provoke = must have, there should be no reason why this isn't on your bar at all times.
Colvanesnce= very good should have it on your bar at all times. Healers get into pinches and this can actaully help save you.
Flash = ultility depends on what type of player you are, if you can do without a circle aoe aggro move other than steel cyclone then you can consider swaping this skill out for something else. I keep it on the bar personally at all times since there's alot of tricks I can do with flash to obtain quick aggro when I need it.
Internal release = can go to increasing your dps and trust me more statics out there are turning their wars into war dps on high end content so consider this skill.
Mantra = useful for aoe heal heavy fights.

Since I fight in coil and ex primals alot this is what I use.

Anyway just my two cents pretty sure one person in this thread is going to tell you a different set they use, the thing is there's no one size fits all cross class skill set for warrior.