Let assume, that I have a group of prime order $p-1$ denoted as $Z_p$. From this group I generate randomly two sets of numbers: $\{x_1, x_2, x_3, x_4, x_5\}$ and $\{y_1, y_2, y_3, y_4, y_5\}$ and compute values $$m_{1} = \prod_{i=1}^{5} x_i$$ and $$m_{2} = \prod_{i=1}^{5} y_i.$$ Let's now assume that I now the values of numbers: $x_1, x_3, x_4$ and $y_1, y_3, y_5$ but I don't know the values of $x_2, x_4, y_2, y_4$. Given all these information, with what probability I can distinguish the values $m_1$ and $m_2$ from values $m_1' = x_1\cdot y_2 \cdot x_3 \cdot y_4 \cdot x_5$ and $m_2' = y_1\cdot x_2 \cdot y_3 \cdot x_4 \cdot y_5$ respectively.
Does the chance of distinguishing these values depends on the size of the group?
Can I somehow describe the distribution of a number which I am randomly taking from the cyclic group?