$\sin^225^o+\sin^245^o+\sin^260^o+\sin^265^o$
$=\sin^225^o+\sin^245^o+\sin^260^o+\cos^2(90^o-5^o)$
$=\sin^225^o+\cos^225^o+\sin^245^o+\sin^260^o$
$=1+\Big(\dfrac{1}{\sqrt2}\Big)^2+\Big(\dfrac{\sqrt3}{2}\Big)^2$
$=1+\dfrac{1}{2}+\dfrac{3}{4}$
$=\dfrac{9}{4}$