The 1, 4 & 5 chord structure only really applies to tunes in a major mode and to the relative minor, providing you use the sharpened 7th degree of the harmonic minor scale to change 5 chord from minor to major. Even then people often like to use chords based on other degrees of the scale to provide variety or to "spice up" the accompaniment.

Many traditional tunes are modal, most commonly dorian or myxolydian. In such cases the 1,4,5 structure does not really apply and you have to be looking for other chords to harmonise such tunes. That is certainly not something you can realistically expect a relative beginner to know about or how to go about harmonising such tunes.