Schmeichel–Hakimi conjecture on exceptional planar graphical sequences

A graphical sequence is planar graphical if it is the degree sequence of a planar graph. Using the shorthand $a^bc^d$ for $b$ repetitions of $a$ followed by $d$ repetitions of $c$, consider the sequences $5^{13}3^1$, $7^15^{17}$, and $7^35^{17}$. Schmeichel–Hakimi conjecture. None of these three sequences is planar graphical. The source states that these are the three unresolved cases remaining after their theorem, so the conjecture is open.