As Moo pointed out, it is separable:
Divide through by $x$, rearrange and integrate to get (I'm doing it all pretty much in one step since it is not considered well-mannered to treat the derivative as fractions, even though it is basically how I carry out the operation, but don't tell anyone!): $$\frac{(1-x^2)}{x}\frac{dy}{dx}=(5-y) \leftrightarrow \int \frac{1}{5-y}dy=\int \frac{x}{1-x^2}dx$$ which gives $$-\ln(5-y)+c=-\frac{1}{2}\ln(1-x^2)$$
If you solve this for $y$, you get your result.