5)

Решение:

Рассмотрим $$\triangle ABC$$ и $$\triangle DEC$$.
1. $$\angle BAC = \angle DEC = 90^{\circ}$$.
2. $$\angle ABC = 58^{\circ}$$.
3. $$\angle BAC = \angle EDC = 90^{\circ}$$.
4. $$\angle ACB = 32^{\circ}$$.
5. $$\angle CED = 90^{\circ}$$.
6. $$\angle DCE = 180^{\circ} - 90^{\circ} - 58^{\circ} = 32^{\circ}$$.
7. $$\angle ABC = \angle DEC = 90^{\circ}$$? Нет.
8. $$\angle BAC = 90^{\circ}$$, $$\angle DEC = 90^{\circ}$$.
9. $$\angle ABC = 58^{\circ}$$, $$\angle DCE = 32^{\circ}$$.
10. $$\angle ACB = 32^{\circ}$$, $$\angle EDC = 58^{\circ}$$.
Значит $$\triangle ABC \sim \triangle DEC$$ по двум углам.
1. $$\angle BAC = \angle EDC = 90^{\circ}$$.
2. $$\angle ABC = 58^{\circ}$$, $$\angle DCE = 180^{\circ} - 90^{\circ} - 58^{\circ} = 32^{\circ}$$.
3. $$\angle ACB = 32^{\circ}$$, $$\angle EDC = 58^{\circ}$$.
Значит $$\triangle ABC \sim \triangle DEC$$ по двум углам.
1. $$\angle BAC = \angle EDC = 90^{\circ}$$.
2. $$\angle ABC = 58^{\circ}$$. $$\angle DCE = 180^{\circ} - 90^{\circ} - 58^{\circ} = 32^{\circ}$$.
3. $$\angle ACB = 32^{\circ}$$. $$\angle EDC = 58^{\circ}$$.
Значит $$\triangle ABC \sim \triangle DEC$$ по двум углам.
$$\frac{AB}{DE} = \frac{BC}{EC} = \frac{AC}{DC}$$.
В $$\triangle ABC$$: $$\angle ABC = 58^{\circ}$$, $$\angle BAC = 90^{\circ}$$, $$\angle ACB = 32^{\circ}$$.
В $$\triangle DEC$$: $$\angle DEC = 90^{\circ}$$, $$\angle DCE = 32^{\circ}$$, $$\angle EDC = 58^{\circ}$$.
Значит $$\triangle ABC = \triangle DEC$$ по стороне и двум углам.
1. $$\angle BAC = \angle EDC = 90^{\circ}$$.
2. $$\angle ACB = \angle DCE = 32^{\circ}$$.
3. $$\angle ABC = \angle DEC = 58^{\circ}$$.
Значит $$\triangle ABC = \triangle DEC$$.
Тогда $$AB = DE = x$$, $$BC = EC$$ и $$AC = DC$$.
Ответ: x = AB