5. (i) Given that $$\frac { 2 z + 3 } { z + 5 - 2 i } = 1 + i$$ find \(z\), giving your answer in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants.
(ii) Given that $$w = ( 3 + \lambda \mathrm { i } ) ( 2 + \mathrm { i } )$$ where \(\lambda\) is a real constant, and that $$| w | = 15$$ find the possible values of \(\lambda\).