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Jim has the very odd habit of walking in straight lines. He walks 30 meters to the east, turns right and walks another 15 meters. Then, he turns right again and walks 50 meters. What is the shortest distance between his starting point and the end point of his walk?

25m

25 m.

How did you get that?

It's hard to explain without a diagram.
Draw one yourself showing the way he walks.
You need to calculate the hypotenuse of a triangle where the other arms are 20m (50-30) and 15m.

Even Pythagoras would find it difficult to explain without a diagram.

See Jeff Clark's Math in the Movies.

It is all well and good if Jim is walking in 2-D but not so clear if he is walking on a sphere [like Earth]. The shortest distance will then be calculated from the great circle that passes through both points.

If he was walking on another spherical object in a different galaxy which happened to be 5 metres in circumference, each leg of his journey would return him to his original position and his shortest distance home would be zero metres.

Jim isn't that much of an oddball anyway as everyone walks in straight lines - even if they are infinitely short.

Jim must be a tradesman talking to his mate on the phone

It forms a basic 3 4 5 right angle triangle. (Pythagoras)
The two sides are in the ratio 3:4 ( 15:20) so the hypotenuse is 5 (25)