Triple nested loop where outer and inner loop are dependent on n
In general, I am wondering if this approach of multiplying the iterations of each loop is a good approach to solving worst case running time and big-Theta estimates.


Basically, yes. But you don't really multiply: As explained here at length, you have nested sums. In your case,

$\qquad\displaystyle \sum_{i=1}^n \sum_{j=1}^{10} \sum_{k=n}^{n+5} 1$

(if we count the number of assignment operations) is easy to evaluate because the loops do not depend on each other. It looks like multiplication here, but if you get things like

  for i = 1 to n
      for j = 1 to i
          foo


that does not work anymore.

Note that worst-case considerations and asymptotics do not enter the picture here.