Here's where having a teacher helps a lot. I started out as an adult beginner, and I remember that in one of the first study books (Duvernoy or Burgmuller), there was a passage in the left hand with a sequence of six eights, it went like C-F-Bb-F-A-F. Because of the slow tempo, I could have easily done it 5-1-5-1-5-1, where my thumb would just repeat the F, and my pinky would go down the C-Bb-A sequence. This is where my teacher stepped in - he told me that this is a great learning opportunity, and I should play it 5-1-4-1-5-1, fifth finger on the C, fourth over it to the Bb, fifth to the A. The main reason was that this would be more comfortable at higher speeds, but also that it would allow to do a finger legato on the sequence of three notes.

A lot of the fingering remarks at this stage were about legato. In the easy Beethoven Sonatina in G, you have sort of a reversal of my earlier story - the downward movement is in the top notes here. There's a sequence of two chords, D-A and D-G in bar three. You could easily do both of those 51-51, but then the possibility of joining the two upper notes would be lost. The "correct" fingering would be 51-52, lifting the pinky and doing a nice legato on the top notes, one that follows into bar 4 with 53. It makes a world of difference when you hear how it sounds with a proper chord legato applied.

If you don't have a teacher, the next best thing would be to make sure you have a good edition with the proper fingerings added. Something like Alfred Masterwork, or the newer Schirmer Performance - both are relatively inexpensive and nicely edited. But then you will get just the fingering without the reasoning behind it.