To simplify the expression, we need to rationalize the denominators.

For the first term, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is √5 + √3:

(4√2)/(√5-√3) * (√5 + √3)/(√5 + √3) = (4√2(√5 + √3))/((√5)^2 - (√3)^2)
= (4√2(√5 + √3))/(5 - 3)
= (4√2(√5 + √3))/2
= 2√2(√5 + √3)

For the second term, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 2√6 - 5:

1/(2√6+5) * (2√6 - 5)/(2√6 - 5) = (2√6 - 5)/(4(√6)^2 - 5^2)
= (2√6 - 5)/(24 - 25)
= (2√6 - 5)/(-1)
= -2√6 + 5

For the third term, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 3 - √10:

2/(3+√10) * (3 - √10)/(3 - √10) = (2(3 - √10))/((3)^2 - (√10)^2)
= (6 - 2√10)/(9 - 10)
= (6 - 2√10)/(-1)
= -6 + 2√10

Now, we can substitute these simplified terms back into the original expression:

2√2(√5 + √3) + (-2√6 + 5) - (-6 + 2√10)

Simplifying further:

2√2√5 + 2√2√3 - 2√6 + 5 + 6 - 2√10

Combining like terms:

2√10 + 2√6 - 2√6 + 2√5 + 5 + 6

Simplifying further:

2√10 + 2√5 + 11

Therefore, the simplified expression is 2√10 + 2√5 + 11.