My grandfather gave me an accordion and it has 60 basses (5x12), which I find for a bit unusual.
I cannot find the chart for such accordion. Anyone knows what kind of accordion is this and where I can find the basses chart?
60 basses is bog standard for small accordions. The central diagonal around the specially marked C bass has notes E-C-c-cm-c7 (upper case letters are single notes, here bass notes, lower case are chords). c is C-E-G (inversion is determined by where the chord octave is), cm is C-E♭-G, c7 is what is actually called gdim on a six-row bass, namely E-G-B♭ (for most music using alternating basses you would not notice the difference to the six-row c7, namely C-E-B♭).
Going upwards is "adding sharps", C-G-D-A-E-B-F♯-C♯, going downwards is "adding flats", C-F-B♭-E♭-A♭-D♭. It's not precicely defined which 12 notes are available in the central role (well, all of them when ignoring enharmonics, but an enharmonic switch requires a jump across 12 diagonals).
I know almost nothing about accordions, but I did find a fingering chart that includes 60 bass.
There seem to be many models that have 60 bass keys so you need to give more information for that part of the question.
The most detailed and complete 60 bass accordion chart/diagram I've found is this: https://accordionchords.com/stradella-bass-layouts/60-bass-accordion-chart/
It shows all single notes played by each button and a list of all available and unavailable chords you can play.