5.6. $\sin \left(15^{\circ}+x\right)+\sin \left(45^{\circ}-x\right)=1$.

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5.6. $\sin \left(15^{\circ}+x\right)+\sin \left(45^{\circ}-x\right)=1$.
5.6 Using formula (4.19), we get $2 \sin 30^{\circ} \times$ $x \cos \left(15^{\circ}-x\right)=1 ;$ since $\sin 30^{\circ}=0.5$, then $\cos \left(15^{\circ}-x\right)=1$, or $\cos \left(x-15^{\circ}\right)=1$, from which by formula (5.9) we find $x-15^{\circ}=360^{\circ} k$

Answer: $x=15^{\circ}+360^{\circ} k, k \in Z$.