For 2) split the sum (a+d)/sqrt(bc) + (a+c)/sqrt(de) + (b+e)/sqrt(cd) + (b+d)/sqrt(ae) + (c+e)/sqrt(ab) into two sums
(a/sqrt(bc) + b/sqrt(cd) + c/sqrt(de) + d/sqrt(ae) + e/sqrt(ab)) +
(a/sqrt(de) + b/sqrt(ae) + c/sqrt(ab) + d/sqrt(bc) + e/sqrt(cd))
Now invoke the Arithmetic Mean Geometric Mean inequality, which states that for any set of n non-negative real numbers {x1, x2, ..., xn}, their sum is greater than or equal to n times the nth root of their product, with equality only when all the xi's are all equal. This gives you
a/sqrt(bc) + b/sqrt(cd) + c/sqrt(de) + d/sqrt(ae) + e/sqrt(ab)
≥ 5 * (abcde/(sqrt(bc)*sqrt(cd)*sqrt(de)*sqrt(ae)*sqrt(ab))^(1/5)
= 5 * (abcde/sqrt(a^2 b^2 c^2 d^2 e^2))^(1/5)
= 5 * (abcde/abcde)^(1/5)
= 5 * (1)^(1/5)
= 5
By the same argument, the other sum a/sqrt(de) + b/sqrt(ae) + c/sqrt(ab) + d/sqrt(bc) + e/sqrt(cd) is also greater than or equal to 5. Therefore the minimum value of (a+d)/sqrt(bc) + (a+c)/sqrt(de) + (b+e)/sqrt(cd) + (b+d)/sqrt(ae) + (c+e)/sqrt(ab) is 10.