To understand Genitive case you can look to Possessive case in English.
Nom. Sing. - рік (year), Nom. Pl. - роки (years), Gen. Sing. - року (it is like "year's" in "New Year's Day"), Gen. Pl. - років (it is like "years'" in "years' experience")
But in Ukrainian Gen. case is used not only for possessive phrases (like дім батьків - parents' house), but in some other situations (http://www.ukrainianlanguage.org.uk/read/unit07/page7-3.htm) including phrases with numbers that ending with 5,6,7,8,9,0.
"вам" in Ukrainian can be used as "you" for plural form or a singular polite form (should be capitalized, like "Sie" in German). Technically it fits, but in our case both options are doubtful as plural means you ask a group of people about their age and singular means you talk to supposedly 6-years old as if it's elderly or privileged person.