Recovering a sine curve and solving on a stretched interval

The curve \(y=a\sin(bx)+c\), where \(a\), \(b\) and \(c\) are constants and \(b>0\), passes through \((0,3)\) and is increasing there. Its maximum value is \(7\) and its period is \(\dfrac{4\pi}{3}\).

1. Find \(a\), \(b\) and \(c\), explaining how you decide the sign of \(a\).[3]
2. Find, in terms of \(\pi\), all the values of \(x\) in \(0\le x\le 2\pi\) for which \(y=5\).[4]