To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, we calculate the exponentiation:
5^3 = 5 * 5 * 5 = 125

Next, we perform the addition inside the parentheses:
64.19 + 26.3 = 90.49

Now, we multiply the result by 125:
125 * 90.49 = 11,311.25

Finally, we calculate the exponentiation:
2^10 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 1,024

Now, we subtract 1,024 from 11,311.25:
11,311.25 - 1,024 = 10,287.25

Therefore, the result of the expression 5^3.(64.19+26.3)-2^10 is 10,287.25.