To simplify this expression, we will first evaluate the exponents:

5^0 = 1
27^-7 = 1/27^7
125^-6 = 1/125^6
5^1 = 5

Now we substitute the values back into the expression:

1 (1/27^7) / (1/125^6) 5

Now, simplify the division of fractions:

1 (1/27^7) (125^6) * 5

Next, simplify the exponents:

1 1/(3^7) 5^4 * 5

Now, compute the result:

1 1/(2187) 625 5
= (625/2187) 5
= 3125/2187

Therefore, the simplified result of the expression 5^0 × 27^-7 / 125^-6 × 5^1 is 3125/2187.