DO anyone know how much 4-5 BIG BOXES WILL COST TO SHIP?

I ORDERED THE 25 PACK OF LARGE BOXES FROM USPS TO SHIP AT A FLAT RATE AND THEY ARE EXTREMELY SMALL. i'M MOVING FROM ST PAUL MN TO HOUSTON TX AND I'M THINKING WILL IT BE EASIER TO SHIP 4-5 REALLY BIG BOXES?I'M ONLY TRYING TO SPEND $300-$500 FOR SHIPPING AND I'M MOVING A SMALL STUDIO AND I HAVE NO FURNITURE. IT'S MAINLY CLOTHES, BOOKS,PERSONAL ITEMS ETC. I DO NOT KNOW ANY WEIGHT OR LENGTH OR ANYTHING I JUST WANT A GUEST ESTIMATE, OR THE BEST WAY TO SHIP! I WILL BE TRAVELING GREYHOUND!