You have a 3 digit number. So there are 1's , 10's, and 100's.

Let x;y;z denote integer placeholders.

(1000x + 100y + 10z + 5) - (100x + 10y + z) = 3074

10(100x + 10y + z) - (100x + 10y + z) = 3074 - 5

9(100x + 10y + z) = 3069

(100x + 10y + z) = 341

So our original number was 341.

Artie concatenated a 5 which made it 3415

The difference between 3415 and 341 must give us 3074, and it does, so we have solved the problem