Let us do things one tiny little step at a time.
You say "I know how to calculate the rightmost digits." Does that mean you can just imagine this is possible? Or does it mean that you have successfully entered my one line of Mathematica without the tiniest change of any kind and were able to successfully have Mathematica calculate the last ten thousand digits of your number.
If you are able to enter expressions and think Mathematica might be correctly calculating them then can you enter this EXACT expression, not the tiniest change of any kind, no notebook, no saving, no clicking on anything, just type EXACTLY this and try to evaluate it and see what you get:
Mod[PowerMod[96717311574016,16777216^4*8^4*7*2,10^10]*7^11,10^10]
and evaluate that and get a 10 digit answer back? Is that answer 9497422848? I think that should be the last 10 digits. If you can get the same thing I get then you and I are at least able to get you that far.
You say "Also clicking five minutes.nb in my notes doesn't actually open it." Where did this notebook come from? Did you make that? Do you remember and can you tell me EXACTLY what you put in that and how you saved that? I'm thinking it is really unlikely that you can remember the precise details of every step of doing that. Do you even think you know what is in it? EXACTLY what steps did you use to create that? Why did you make a notebook? Did you then "save" that notebook onto your computer? How? Are you even using "a computer"? Or is it a tablet or is it a phone? What brand of thing is this? If you forget "a notebook" for a minute, are you able to enter a SIMPLE mathematical expression using EXACTLY correct Mathematica syntax and capitalization and get it to give you a correct answer? Can you then enter more simple expressions and get it to give you correct answers? Do you know how to get your computer to tell you how many bytes or gigabytes in size a file is? Can you me tell how big your "five minutes.nb" file is? If it is small, less than a thousand bytes, then can you post here and attach that notebook to your post? At the bottom of the screen when you are posting there is "Attachments" followed by "Add a file to this post." I don't want you attaching something gigabytes or even kilobytes in size, but if your "five minutes.nb" is tiny and you can attach it then I will with great hesitation and caution try to download it without it potentially taking over and destroying my computer and I may risk trying to peek inside it to see if it is a simple ordinary notebook with a simple expression in it that will calculate the last ten thousand digits that you want.
IF you can do all this successfully and repeatedly then you and I have made great progress.
Then you change the problem again and want something COMPLETELY DIFFERENT, you want the leading digits and not the trailing digits. I'm not even sure I can imagine how to do that using only a small finite precision. Can you imagine a way of EXACTLY doing that? Maybe something that works from right to left and only keeps the latest 10 digits as you try to raise each succeeding digit to the 16777216^4*8^4*7*2 power?!?! But I find it very difficult to imagine doing that. Can you think of how to raise a single digit to that power and save the leftmost dozen digits and do that with each of the digits of 96717311574016 and then we somehow try to reassemble those leftmost dozen digit pieces? I'm VERY skeptical that this might even be possible? I can estimate your result is more than 6 times 10^34 power DIGITS and I can't even suggest you learn another programming language and buy yourself a huge hard drive to store the calculation in progress, that will never fit.
So, before trying to do that, let us see if we can get you dependably calculating much simpler things. Then we can make the tiniest little steps so you can possibly trust that you can do things on your own.