First, let's expand the expression:

(√5-2)² = (√5-2)(√5-2)
= (√5)(√5) - 2(√5) - 2(√5) + 2(2)
= 5 - 2√5 - 2√5 + 4
= 9 - 4√5

Next, (√5-1)×(√5-3)
= (√5)(√5) - (√5)(3) - 1(√5) + 3
= 5 - 3√5 - √5 + 3
= 8 - 4√5

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

(√5-2)² - (√5-1)×(√5-3)
= 9 - 4√5 - 8 + 4√5
= 1