This plugin is compatible with Font Awesome 4, not with 5.
Here's what you need to change in jquery.raty-fa.js to make ik Font Awesome 5 compatible:
$.fn.raty.defaults = {
cancel : false,
cancelHint : 'Cancel this rating!',
cancelOff : 'fas fa-fw fa-minus-square',
cancelOn : 'fas fa-fw fa-check-square',
cancelPlace : 'left',
click : undefined,
half : false,
halfShow : true,
hints : ['bad', 'poor', 'regular', 'good', 'gorgeous'],
iconRange : undefined,
mouseout : undefined,
mouseover : undefined,
noRatedMsg : 'Not rated yet!',
number : 5,
numberMax : 20,
precision : false,
readOnly : false,
round : { down: .25, full: .6, up: .76 },
score : undefined,
scoreName : 'score',
single : false,
size : null,
space : true,
starHalf : 'fas fa-fw fa-star-half-alt',
starOff : 'far fa-fw fa-star',
starOn : 'fas fa-fw fa-star',
target : undefined,
targetFormat : '{score}',
targetKeep : false,
targetText : '',
targetType : 'hint',
width : false
};