Difficulties with a stochastic variable

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.