Problem 149

### Step-by-Step Solution

#### Problem (1): $-20+3+5-7$

- Start by adding and subtracting the numbers in order:
$$-20 + 3 + 5 - 7$$
- Combine the positive numbers and then the negative ones:
$$= (-20 - 7) + (3 + 5)$$
- Simplify the operations:
$$= -27 + 8$$
- Finally, add the results:
$$= -19$$
- So, the answer is $\boxed{-19}$.

#### Problem (2): $(-32)÷4×\frac{1}{4}$

- Begin by dividing $-32$ by $4$, then multiply by $\frac{1}{4}$:
$$=(-32) ÷ 4 × \frac{1}{4}$$
- Perform the division first:
$$= -8 × \frac{1}{4}$$
- Then, multiply by $\frac{1}{4}$:
$$= -2$$
- Therefore, the answer is $\boxed{-2}$.

#### Problem (3): $(\frac{2}{7}-\frac{1}{4})×28$

- Start by finding the common denominator and subtracting the fractions:
$$= \left(\frac{2}{7} - \frac{1}{4}\right) × 28$$
- Convert $\frac{1}{4}$ to $\frac{7}{28}$ and $\frac{2}{7}$ to $\frac{8}{28}$, then subtract:
$$= \left(\frac{8}{28} - \frac{7}{28}\right) × 28$$
- Simplify the fraction and multiply by $28$:
$$= \frac{1}{28} × 28$$
- The result is:
$$= 1$$
- Hence, the answer is $\boxed{1}$.

#### Problem (4): $-{2}^{4}×[(-3)×(-2-1\frac{1}{3})-(-5)]÷{(-\frac{2}{5})}^{2}$

- Begin by simplifying the expression inside the brackets and the exponent:
$$= -16 × [(-3) × (-\frac{10}{3}) - (-5)] ÷ \frac{4}{25}$$
- Simplify the multiplication and addition inside the brackets:
$$= -16 × (10 + 5) × \frac{25}{4}$$
- Multiply the numbers:
$$= -16 × 15 × \frac{25}{4}$$
- Simplify to find the final result:
$$= -1500$$
- Therefore, the answer is $\boxed{-1500}$.