I wonder if the sizes you were given were in non-U.S. sizes :?:
"Size 4 or 5" could additionally mean UK English or Metric sizing. Given the weight of the yarn and the number of stitches, if I were you, I'd try a US size 8. The reason why may become apparent to you after a closer look at the conversions below:
U.S.: 5, 6, 7, 8, 9, 10
English: 8, 7, 6, 5, 4, 3,
Metric (mm): 3.75, 4.25, 4.5, 5.0, 5.5, 6.0
I've worked a few hats by "winging it" on circulars and straights and in combination. Cheer up, I've yet to use a pattern that worked for me either! Of course, I've yet to try any of the great hat patterns here yet, so we'll see later because there's a first time for everything!
First, cast on the 72 stitches and then wrap it around your head to see if you're in the ball park. Adjust your needle size accordingly. You should be within an inch or two of the correct sizing for it to work right. Too long? Try a size 7 and fit again. Too tight? Try a size 9.
Also keep in mind that your ribbing will allow for some tightness around the temple and there'll also be some give built into it as well.
The instructions I give you below is roughly what I did with my first hat pattern and a few subsequent ones. So let's keep it simple and enjoy a rewarding first time hat making experience. Read on.
When you work on the right length circulars, the stitches should tighten up as you go around (usually after 5-10 rounds). If it doesn't tighten for you, you can always tighten up your stitches a bit at a time at each new round or until you think you've got about the right diameter.
Then ease up on the tension and keep working the same amount of stitches until you get the length you want. Be sure to end at your 72nd stitch.
Then simply leave a long tail (like a foot or two to be extra safe) and grab a yarn needle and thread it with the long tail. Beginning at stitch #1 on your last worked row, cast off by threading each loop on your circular through the yarn needle as you slide them off and onto the long tail. Once they're all off the needle, pull your threaded/looped circle as tightly as possible and weave in the end on the wrong side of your hat.
I sure hope this is helpful for you! Good Luck!