Step 1:
$5x^2+10x+9y^2-36y=4$
Completing squares,
$5(x^2+2x+1)+9(y^2-4y+4)=4+5+36$
$5(x+`)^2+9(y-2)^2=45$
Step 2:
Dividing the above equation by $45$ we get
$\large\frac{(x+1)^2}{9}+\frac{(y-2)^2}{5}$$=1$
$a^2=9,b^2=5$
$\Rightarrow a=3,b=\sqrt 5$
Step 3:
Length of major axis = $2a=2\times 3=6$
Length of minor axis = $2b=2\times \sqrt 5=2\sqrt 5$
Equation of major axis =$y = 2$
Equation of minor axis =$x = -1$