Where did you get 5 or 6 percent? I found the following reference:
"Under the Union draft act men faced the possibility of conscription in July 1863 and in Mar., July, and Dec. 1864. Draft riots ensued, notably in New York in 1863. Of the 249,259 18-to-35-year-old men whose names were drawn, only about 6% served, the rest paying commutation or hiring a substitute."
A quarter million men were raised on the Union side due to the Draft. Some were draftees, most were so-called "substitutes", and undoubtedly some never reported. A quarter million men that you wouldn't have had without the Draft. Considerably more than 6 percent of the total standing force of the combined Union Armies at any given instant in 1864/5 wouldn't you agree?
Sure. And all Five Point hookers looked like Cameron Diaz, too.
Cute. Do you have any hard stats, or are you just blowing smoke?
Not quite. In a Union army of 2.5 million, 6% would be 150,000 men or about 60% of those you site says were called up. Your site mentions commutations and substitutes as ways of avoiding service. Commutation was simply paying a specific amount of money, usually several hundred dollars, and the draftee is released from their obligation. Such a practice resulted in no soldier at all. Also your site doesn't mention the fact that conscripts could be release for hardship or because of disability. This site mentions that in 1863 some 65% of all conscripts were released due to physical disability or hardship. Between commutation and other forms of discharge it's not hard to see how the draft actually produced comparatively few soldiers.