You have stumbled across the PENTATONIC SCALE. Of which there are two - major and minor. Ascending, by starting on F#/Gb, you have the major pent., start on D#/Eb and it's the minor. The five notes (hence pent!) work well and harmoniously together, with nothing that clashes (is dissonant).
These notes work well together, as the 'avoid notes' as we call them, are actually avoided - from the full major and minor scales. In F#, those notes are the 4th and 7th, B and E# respectively. Played together,they produce the Devil's interval, thought to be dissonant for many centuries. Although now often used in Blues music. On that tack, by adding the flattened 5th (A) the pent turns into the Blues scale.
There are many tunes that only use the pentatonic scale notes, Amazing Grace being one of the best known. Although the harmony to most of these tunes will include the avoid notes. Google 'Penatonic melodies'. Please note that they may well NOT be in the key which is quoted - F#/D#m - but will still only contain the appropriate notes, but in other keys - and can still be played purely on the 'black keys' on a keyboard.