Try giving the attribute HoldFirst:
SetAttributes[fivetries, HoldFirst]
fivetries[arg_] := Table[arg, 5]
fivetries@RandomReal[]
This way the RandomReal is evaluated last, after the Table.
fivetries@Unevaluated@RandomReal[] also works, but I would use HoldFirst or HoldAll as Gianluca shows.
Note Attributes@Table includes HoldAll, which is why the argument RandomReal[] in Table[RandomReal[],5] is not evaluated first; instead, it is evaluated when Table[] is ready to evaluate it.