A planetary gear train of an automatic transmission for a vehicle is provided to improve power delivery and fuel efficiency by applying six engaging elements to five planetary gear sets to achieve ten forward speed stages and one reverse speed stage. The planetary gear train includes: an input shaft; an output shaft; first to fifth planetary gear sets each including three rotation elements; three clutches and three brakes as the six engaging elements; and first to ninth shafts. In particular, the third shaft fixedly connects seventh, tenth and thirteenth rotational elements, and the fourth shaft fixedly connects sixth and fifteenth rotational elements. In addition, the fifth shaft fixedly connects third and fourth rotational elements, the sixth shaft fixedly connects fifth and eighth rotational elements, and the seventh shaft fixedly connects ninth and eleventh rotational elements.