I can't remeber witch but I'm almost sure that in a episode in the middle या in the end of season 4 Booth says he's 7.. So I think he turned 7 in season 4 but he was 6 in "The finger in the nest"
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And Booth says he's 4 in season 1 and if every season is ca. 1 साल then he probably turns 7 in the end of season 4 ;)