$a)\left(\left(-\infty ;5\right)\cup \left[5;7\right)\right)\cap N=\left(-\infty ,7\right)\cap N=\left\{0,1,2,3,4,5,6\right\}$  

 

$b)\left(\left(-\infty ;5\right)\cap N\right)\cup \left(\left[5;7\right)\cap N\right)=\left\{0,1,2,3,4\right\}\cup \left\{5,6\right\}=\left\{0,1,2,3,4,5,6\right\}$  

 

$c)\left(N\backslash \left(7;\infty \right)\right)\cap \left[0;\infty \right)=\left\{0,1,2,3,4,5,6,7\right\}\cap \left[0;\infty \right)=\left\{0,1,2,3,4,5,6,7\right\}$  

 

$d)\left(N\cap \left[0,\infty \right)\right)\backslash \left(\left(7;\infty \right)\cap \left[0;\infty \right)\right)=N\backslash \left(7,\infty \right)=\left\{0,1,2,3,4,5,6,7\right\}$  

 

$e)\left(\left(-3;7\right]\cap \left(0;10\right)\right)\cup \left[5;9\right)=\left(0,7\right]\cup \left[5;9\right)=\left(0,9\right)$  

 

$f)\left(\left(-3;7\right]\cup \left[5;9\right)\right)\cap \left(\left(0;10\right)\cup \left[5;9\right)\right)=\left(-3,9\right)\cap \left(0,10\right)=\left(0,9\right)$  

 

$g)\left(C\cap \left[-5;7\right]\right))\backslash N=\left\{-5,-4,-3,\dots ,6,7\right\}\backslash N=\left\{-5,-4,-3,-2,-1\right\}$  

 

$h)\left(C\backslash N\right)\cap (\left(\left[-5;7\right]\cap N\right)=C_{-}\cap \left\{0,1,2,3,4,5,6,7\right\}=\varnothing$