At 5 he can learn how to ski, but it sounds to me like you are expecting alot. Children will learn at their own pace. Find a hill with a nice gently sloped magic carpet and let him play there for as many weeks as it takes for him to be comfortable going up and down the gentle slope and learn to turn both directions. My first child (pre my b eing an instructor), i took out to a ski clinic at 2.5 years and thought the ski instructors were morons as after 8 weeks he couldn't ski. 2 years later when I started to teach I learned a little better. My first son never liked skiing, probably from my expectations early on and his inability to please us and knowing it, no matter how much we said it's okay. He heard us talking a bout the instructors etc. So be really careful
My second son, had the benefit of 3 years of teaching experience under my belt when I started him at 4.5 yrs. By then I had learned that children under 5 rarely actually learn to turn and ski and rarely hold what they learned from year to year if they do learn. So he played in the kinder ski play ground for 2 years (wooden figures and snow climbers on flat ground), until at 4.5 I decided I had kept him active enough to devleop the necessary muscle control (something I didn't do with the first) to learn how to turn and ski. He was also desperate to go up the hill with his now 7 year old brother and us. He learned to turn and ski in hour and loved it forever. His brother never got good, you could tell never really enjoyed it and at 10 we swtiched him to snow boarding.
So, make sure you son does lots of active play to build muscle and balance control. This would be climbing monkey bars at parks, lots of time up and down slides on his own, running and walking lots when you're out. Build his stamina and muscle control, it will make a huge difference to how long he can sustain the effort needed to learn to ski. A protein rich diet that helps build muscle would also help. Really skinny legged children (i know it's genetic typically), typically but not always, can be difficult to teach. Lack of muscle development being the culprit. They can learn, just takes a little more time as they have to learn to be gentle and finesse the skis to move them and can't rely on muscling their way out of situations. The same holds true for adults btw, work out, develop the leg muscles some prior to starting and it will make a difference.
For now, go play with your son at the hill, realize before you go that the patience you need is at least equal to the patience you needed to toilet train him and go only for a morning or afternoon and not on a day you will want to go ski. Go and just play with your son that day on the beginner hill. Ski for yourself another day, not that day and the effort you put in to making your son enjoy his time (lots of stops for hot chocolate to warm up), stopping and going home if your son wants to, so he knows he can say, i'm not into this today with no worry, will help him enjoy it and learn. The one on one time for your son will also go a long way.
Group lessons might be okay for him if he likes the social aspect. If he feels pressure as he's not doing as well as the other kids he may just hate it more. Never bribe him to stay on the hill, let him have a break and stop when he wants. It is wise to let someone else teach your child and if you did put him in lessons, i'm sure the hill would put him with a suitable instructor if he was still having difficulty over the group. I was often the instructor at my home resort who took the children and adults from group lessons when they had difficulty learning and did lessons with them for a couple weeks to catch them up to the group or in some cases, I just got to keep those having difficulty learning, and work with them for the rest of their 8 week program. Btw, they all learned how and caught up, I never had someone that just couldn't learn. So patience and time dedicated to your son, with no expectations and lots of cheering and high fives for small feats (wedges, accidental turns, etc), and lots of time running around in skis and walking up slight hills in skis (this teaches pressure control and balance really well), will have your son going in what will feel like no time and be less frustrating for you all and more fun when you get small gains.
Oh, one other helpful tip. When i taught my grand daughter 3 weeks ago, I brought her dad, my husband and me. We all took turns with her through the day after I gave her the basic lesson and got her turning. This way all of us got to ski and she got a fresh person to relax and have fun playing on the snow with. So if you can enlist a couple friends that like kids, do it.