$\sqrt{(14+6\sqrt{5})}—\sqrt{(9—4\sqrt{5})}=\sqrt{(5+6\sqrt{5}+9)}—\sqrt{(5—4\sqrt{5}+4)}=\sqrt{(\sqrt{5}+3{)}^2}—\sqrt{(\sqrt{5}—2{)}^2}=|\sqrt{5}+3|—|\sqrt{5}—2|=\sqrt{5}+3—\sqrt{5}+2=5$