Thank you for sharing the image! Let’s analyze the diagram and solve for the required angle.

Problem Breakdown:

1. We are given that $\angle ABC = 74^\circ$.
2. The diagram is a quadrilateral split into multiple smaller triangles. We aim to calculate $m\angle 5$, which corresponds to $\angle AED$.

Observations:

• Points $A, B, C, D$ are connected with intersecting diagonals $AC$ and $BD$, meeting at $E$.
• Triangles are formed around $E$: $\triangle ABE, \triangle BCE, \triangle CDE, \triangle ADE$.
• $\angle ABC = \angle 2 + \angle 3$.

Solution:

Since $\angle ABC = 74^\circ$:

1. Determine relation of $\angle AED$ to given angles:

   • Using triangle properties and linear pairs, $\angle 5 = \angle AED$ can be computed based on internal angles at $E$ and the symmetry of quadrilateral properties.

2. Geometry principles at play:

   • Adjacent angles $\angle AED, \angle AEB, \angle BEC,$ and $\angle DEC$ around point $E$ sum to $360^\circ$.

Using geometric properties and symmetry of the diagram, $m\angle 5$ can be computed as follows:

$\text{Final calculation pending based on context from the geometry rules in the image.}$

If you confirm a specific symmetry relationship, I can refine further! Let me know!