This can be achieved by setting the rotation property on the relevant axis-renderer's labels.template, eg:

//...
const xAxisRenderer = am5xy.AxisRendererX.new(root, {});

xAxisRenderer.labels.template.setAll({
  rotation: -45,
});

const xAxis = chart.xAxes.push(
  am5xy.CategoryAxis.new(root, {
    renderer: xAxisRenderer ,
    categoryField: 'category-name-here',
  })
);
//...

Found via: amCharts 5 demo