To simplify the expression (3/5)^15 : (0.36)^5, we can first rewrite the numbers as decimals:

(3/5)^15 = 0.6^15
(0.36)^5 = 0.36^5

Now, we can calculate the values:

0.6^15 ≈ 0.000137
0.36^5 ≈ 0.07776

Finally, we can divide the two values:

0.000137 / 0.07776 ≈ 0.00176

Therefore, (3/5)^15 : (0.36)^5 is approximately 0.00176.