Yes, there are button holes later in the pattern. This seems like a button hole right in the middle of the back, but am I reading it wrong? I did try it and there’s a hole! Where it says “turn” it is a type of short row, right? I have put the whole pattern in with the button hole instructions, below. Really appreciate your help.
PETER PAN COLLARED JUMPER BACK With 3mm (US 2-3) needles and M cast on 63(67:71:75) sts. K 5 rows. Change to 3.25mm (US 3) needles. Beg with a k row, work in st st until back measures 16(18:20:22)cm/6¼(7:8:8¾)in from cast on edge, ending with a p row.
Back opening
Next row K29(31:33:35), turn and cast on 5 sts. 34(36:38:40) sts. [AM I KNITTING THIS SEPARATELY FROM THE NEXT ROW? LIKE TIE ON ANOTHER BALL OF YARN?] DONT LAUGH! 
Next row K5, p to end.
Next row K to end. Rep these 2 rows until back measures 24(26:28:30)cm/9½(10¼:11:11¾)in from cast on edge, ending at armhole edge.
Shape shoulder
Cast off 6(6:7:7) sts at beg of next and foll right side row. 22(24:24:26) sts. Work 1 row. Next row Cast off 5(6:6:7) sts, k to end. Next row P to end. Leave rem 17(18:18:19) sts on a spare needle. Mark position for 3 buttons, the first to come in the first row of neckband, and two more spaced 3cm/1¼in and 6cm/2¼in from first buttonhole.
Work buttonholes to match markers as folls: Buttonhole row (right side) K1, k2tog, yf, k to end. With right side facing, rejoin yarn to rem sts, k to end. 34(36:38:40) sts.
Next row P to last 5 sts, k5. Next row K to end. Working buttonholes to match markers rep these 2 rows until back measures 24(26:28:30)cm/ 9½(10¼:11:11¾)in from cast on edge, ending at armhole edge. Shape shoulder Cast off 6(6:7:7) sts at beg of next and foll wrong side row. 22 (24:24:26) sts. Work 1 row. Next row Cast off 5(6:6:7) sts, p to last 5 sts, k5. Next row K1, k2tog, yf, k to end. Leave rem 17(18:18:19) sts on a spare needle.