To find out how much each cousin inherited, we need to divide the total fraction of assets they inherited by the number of cousins.
The total fraction inherited by the six cousins is \(\frac{5}{8}\).
To find out how much each cousin received, we divide \(\frac{5}{8}\) by 6:
\[ \text{Amount inherited by each cousin} = \frac{5}{8} \div 6 = \frac{5}{8} \times \frac{1}{6} = \frac{5 \times 1}{8 \times 6} = \frac{5}{48} \]
So, each cousin inherited \(\frac{5}{48}\) of their great aunt's assets.
Therefore, the answer is:
\(\frac{5}{48}\) of the assets.