I don't know, if the formula that is available will be "clearer", but I can give you some background information to that expression.
There are in principle two alternatives:
1.) You can split the 10th order function into 5 separat transfer functions - each of 2nd order. For each of this functions you can use a delay formula that is available (expressed in terms of pole frequency and damping resp. pole Q). The final delay function then is the sum of the 5 delay functions.
2.) There is another formula based on the pole location of the 5 pole pairs. Thus, the delay formula consists of the sum of 5 expressions - each containing the real part of the respective pole and the squared magnitude of the difference (w-Sn), with Sn=pole location.
As you will see, it's relatively complicated and I doubt if it really helps.
Nevertheless, if you are interested I can give you details (tell me if to 1) or 2)).
LvW