5. Solution: Because the triangle ABC is an equilateral triangle (known), AB=AC (the three sides of the equilateral triangle are equal).

Because in triangle ABD and ACE, AB=AC (proved).

Angle 1= Angle 2 (known)

BD=CE (known)

So triangle ABD is equal to ACE(SAS)

So the angle BAD= angle CAE (the corresponding angles in congruent triangles are equal).

So angle BAD+DAC= angle CAE+DAC (equal property)

That is, angle BAC= angle DAE, because angle BAC=60 degrees (known).

So the angle DAE=60 degrees (equivalent replacement)

So the triangle ADE is an equilateral triangle (an isosceles triangle with an internal angle of 60 degrees is an equilateral triangle). 6. Solution: Because angle CBP= angle A+BPA (the property of the sum of the external angles of a triangle) and angle BPA=30 degrees (the property of equality), angle A=BPA (equivalent substitution), so AB=BP (equilateral), because AB=0.5* 2.4= 1.2 (nautical mile).