I'm guessing you mean
[tex]\displaystyle\int\sin^35\theta\cos5\theta\,\mathrm d\theta[/tex]
Let [tex]t=5\sin\theta[/tex]. Then [tex]\mathrm dt=5\cos5\theta\,\mathrm d\theta[/tex]. So we have
[tex]\displaystyle\int\sin^35\theta\cos5\theta\,\mathrm d\theta=\frac15\int\sin^35\theta(5\cos5\theta)\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac15\int t^3\,\mathrm dt[/tex]
[tex]=\dfrac{t^4}{20}+C[/tex]
[tex]=\dfrac{\sin^4\5\theta}{20}+C[/tex]
