To solve the geometric problems presented in the image, we can follow these steps:

### Bài 5:
#### a) Chứng minh ∠ABM = ∠ABN
You can use the property that the angles subtended by the same arc in a circle are equal. If points A, B, M, and N are on a circle, then ∠ABM = ∠ABN.

#### b) Chứng minh AB là phân giác của MAN
You need to show that triangle ABM is similar to triangle ABN, indicating that AB bisects angle MAN.

#### c) Biết ∠MAB = 20°; ∠MBA = 25°
Using these angle values, you can find the remaining angles:
1. ∠MAB + ∠ABM + ∠AMN = 180° leads to finding ∠ABM.
2. Use the known angles to find angle measurements in triangles.

### Bài 6:
#### a) Chứng minh ∠ABM = ∠ACM
Since triangles ABC is isosceles (AB = AC), therefore, ∠ABM = ∠ACM by the properties of isosceles triangles.

#### b) Chứng minh ACM = ABM
You can use the equality of angles in isosceles triangles or the properties of corresponding angles.

#### c) AM ⊥ BC
This can be shown by proving that lines AM and BC meet at a right angle, often using the definition of perpendicular lines.

#### d) Biết AB = 13 cm; CM = 5 cm; AM = 12 cm
Using the Pythagorean theorem, you can determine the length of BM.

### Bài 7:
#### a) Chứng minh ∠ABC = ∠CDA
You would need to prove that these angles are equal using an appropriate geometric property or theorem.

#### b) BAC = ACD; AB / CD
You can show the ratios of the sides relate based on similarity or proportional triangles.

#### c) AD / BC
Again, this would involve demonstrating that these ratios hold under the triangle properties or similarity.

For further calculations and proofs, apply relevant theorems, such as the Triangle Sum Theorem, properties of similar triangles, and Pythagorean theorem as needed.