First, let's expand the expression:

$\surd 5-2$² = $\surd 5-2$$\surd 5-2$ = $\surd 5$$\surd 5$ - 2$\surd 5$ - 2$\surd 5$ + 2$2$ = 5 - 2√5 - 2√5 + 4
= 9 - 4√5

Next, $\surd 5-1$×$\surd 5-3$ = $\surd 5$$\surd 5$ - $\surd 5$$3$ - 1$\surd 5$ + 3
= 5 - 3√5 - √5 + 3
= 8 - 4√5

Now, we can substitute the above results back into the original expression:

$\surd 5-2$² - $\surd 5-1$×$\surd 5-3$ = 9 - 4√5 - 8 + 4√5
= 1