Three fifths of a person was a compromise... an unfortunate compromise, because it left the South with enough power to motivate them to keep on collecting slaves. The most important fact to realize about "three-fifths" is that it only applied to slaves— and slaves were not identified by race (at the time there were white slaves and Native-American slaves in the United States, too). The whole point of the three-fifths compromise was supposed to be that property doesn't vote — if you consider a person to be your property, then you don't get the value-added bonus of counting them toward your representation in the House of Representatives.
The compromise was between the Southerners and the Northerners. The Southerners wanted "One man, One vote" (including men who are property). The Northerners wanted "Got slaves? Get real!" (meaning that you don't become more than one person just because you own other people). The problem with the three-fifths compromise was that a slave-holder counted as one and three-fifths of a person if he owned one slave. He counted as four people if he owned five slaves, and so on.
The compromise was too weak to impact slavery in the United States. "Three fifths" empowered the South to continue slavery, and became an extra motivating factor to prevent slaves from escaping from the South to the North — if your three-fifths-of-a-person-Slave managed to cross the Ohio river, he might suddenly became a five-fifths-freeman. He might actually be allowed to vote for himself rather than being "represented" by the slave-master's vote. If laws existed to allow that free man to stay in a Northern state then the South would start to bleed it's power.
The notion that the founders were slave-holders who had no desire to end slavery upon the foundation of the country is easily debunked. Prior to independence, the British government actually forbade the colonies from eliminating slavery — all of the colonies were forced by Britain to permit slavery. Vermont was the first to abolish slavery in the adoption of its own constitution in 1777 (twelve years before the Constitution was adopted). Technically, however, Britain had not yet recognized the independence of any of the American colonies. The American Revolutionary War was not concluded until September of 1783; yet Pennsylvania, Massachusetts and New Hampshire had already abolished slavery by that time.
Connecticut and Rhode Island had also abolished slavery prior to the ratification of the U.S. Constitution in 1788. Vermont officially joined the United States when George Washington was the President. New York soon abolished slavery during John Adams' presidency. Ohio abolished slavery in its founding constitution and New Jersey abolished slavery during Thomas Jefferson's administration. This meant that slavery had been abolished in all nine Northern states (out of the seventeen members of the United States) by 1804 — just sixteen years into the existence of the United States of America. Slavery was still permitted in England — Great Britain wouldn't abolish slavery for another three years.
So the next time you encounter a person who thinks that this country was founded on slavery and regarded black people as less than a person, just remember that this country led the way toward abolishing slavery, and that the whole point of "three-fifths" was to emphasize that a free black man was a complete person, but a slave, regardless of their color, was less than complete.