#Python, <s>80</s> <s>73</s> 72 bytes

First submission, don't be too harsh q:

0-indexed

    lambda x,y:[(a-1,b//a,b%a)for a in range(25)for b in range(a*a)][70*x+y]

Creates a list of length 4900 with all pyramind coordinates and returns a different list entry for each input.

<a href="https://tio.run/##K6gsycjPM/6fZhvzPycxNyklUaFCp9IqWiNR11AnSV8/USdJNVEzLb9IIVEhM0@hKDEvPVXDyBQskoQQSdRK1IyNNjfQqtCujP1fUJSZV6KRpmGmY6Gp@f//fwA" title="Python 3 – Try It Online">Try it online!</a>