To simplify the expression (1/4 - √125/64), we first need to simplify the square root.

√125 = √(25 5) = √25 √5 = 5√5

Now we can substitute √125 with 5√5 in the original expression:

1/4 - 5√5/64

To subtract these two fractions, we need a common denominator. The common denominator here is 64, so we can rewrite the fractions with this denominator:

16/64 - 5√5/64

Now we can subtract the fractions:

(16 - 5√5)/64

Therefore, the simplified expression is (16 - 5√5)/64.