Hm. As long as it's not all that equipment, and realistic amounts per member, variation then sure, it can work. I might switch my flow up in that case. 

I'll go with two spartans, a Royal Spartan highest of their tier(the general of the band), and a Spartan Hoplite, standard soldier.(Steel curiass(for this generation of combat) protecting chest, upper arms and thighs, steel greaves to the knees, armguards for the forearms and the usual pilos helmet with red transverse horsehair crests on the top to identify rank for the Royal Spartan; weapons include a Xiphos, well made steel sword compared to usual models of the sword at their belt, a Doru spear and a javelin for throwing. Alongside this their original Spartan shield which they always keep near)

A viking berserker (chainmail armor, two handed long ax, medium length straight sword, medium round shield, two throwing axes)

A medieval foot-knight (half plate full armor, morningstar and heater shield, dirk at the belt.)

For the last two they will be a English Yeoman Longbowman (Light leather armor, black cap on the head, full quiver of bodkin arrows, yew longbow and a short sword at the belt) and a ninja (pure black cloth, facemask, ninjato sword at the lower back, kunai knives at the belt, a chain and sickle kusarigama, and the soft cased shell explosives of different types, majorly smoke and carefully packed glass sharpnel pieces inside the ball so upon contact releases many small bits of glass at the opponent, typically the eyes)

If that's alright, limited equipment to realistic standards as-well for the run.