EASY --- LIKELY --- REALISTIC --- UNLIKELY --- IMPOSSIBLE
This is what the "contiuum of goals" might look like.
Where do you fall?
As it was pointed out, it depends on many factors.
AGE... it is a FACT that gaining a large amount of strength becomes a lot harder as you get older. Bak when I was in my 20s adding weight to the bar was easy. I quickly built up to a 270kg squat and 220kg front squat. In my 30s I did lose a lot of that from focusing more on upper body but when I tried to regain it, it took me a lot longer to get about 90% there. In my 40s now it's even more of a challenge and I know that it is not realistic to expect getting back to my old PRs.
Now, some older lifters ARE lifting big weights. But most of them fall in one of these categories:
a) guys who have always been very strong and are either simply maintaining their strength (or part of it) or gaining a small amount. A friend of mine deadlifted 260kg x 3 reps and squatted 240kg at 48 years of age... BUT he did participate the World Weightlifting Championships when he was in his 20s (as a 82.5kg lifter)... back then he clean & jerked 195kg, deadlifted 300kg and squatted 290kg. He was still very strong at 48, but he didn't GET strong , he just maintained some of his strength as he got older.
b) guys who had the potential to be really strong, but never lifted until they were older. These are the freak genetics who could have been world class had they trained when they were young. But because training wasn't popular back then they never picked it up. When they finally start to do it when they are older, they still have a lot of untapped potential that can be revealed even when they are older. BUT this kind of potential is very quickly revealed. At the gym I used to train a guy started training at 45. The first session he failed to bench press 135lbs (I remember because he got stuck there and we had to help him out) but within 8 months he was doing 315lbs... with a family of 5 kids and working 60 hours a week (owned a business). But these guys are not only squatting 105kg after 5 years of training, so we will assume that you aren't in that class.
c) guys taking hormones. While you can slow down the decline in testosterone by living a good life and having luck on your side, it is a fact that testosterone levels drop down as you get older. and as it drops down so does your capacity to build muscle, gain strength and recover from training. An older lifter can make himself "artificially younger" by using anabolic steroids and thus progress at the same rate as a younger fellow (provided that he doesn't get injured).
At 38 you are not yet old in calendar years. But there can still be some wear and tear and maybe some hormonal decrease. But in normal people gaining strength does become harder past 35 and even more so past 40. I don't know how much your squat has improved since you start training, but let's say that it went from 60kg up to your current 105kg in 5 years. So that is roughly 10kg per year. If you were to progress at this exact rate in a linear fashion it would take you 11-12 years to reach your goal. But realistically your possible rate of progress will slow down a few times during those 12 years... once you hit 40, 45 and 50. So you will likely not be able to maintain the same rate of progress for the whole duration and it will even stop at one point and maintenance will be the best outcome. Now, I will give you that it is possible that for the first few years of your training life you might not have known what you were doing or didn't focus on the squat. So maybe your potential rate of progress is closer to 20kg per year... but that still represents 6 years, if you could sustain that optimal (for you) rate, which I doubt can be the case as you are getting older (I can say this because I am in the older category).
GENETIC POTENTIAL FOR STRENGTH: A friend of mine is a strongman competitor and a lot of people come to his gym to become strongmen or powerlift, very few stick with it. We were talking last week and he told me this "not every body has what it takes to be strong"... every body can improver and get stronger, a lot stronger even. But few naturally have what it takes to be at a very high level. And those who naturally have it, we quickly know. Within a few months their strength goes up really fast.
As Judas pointed out, 235lbs after 5 years of training is weird. There might be something going on. At the gym I train at (Crossfit box) you can kick on a trash can and 12 small crossfit girl squatting more than that can fall out!!! My wife is an occasional trainee at best (average of 2 Crossfit session per week) and she full squats 100kg. So you might have some serious technique issues, a glaring muscle weakness holding you back and a low potential for strength.
Everybody easily accept that not everybody has the genetics to be a great basketball player (being 5'7" makes it much harder than being 6'7") but few accept that we don't all have what it takes to be really strong. We can all improve, but only to a point.
STRUCTURE AND CAPACITY TO AVOID INJURIES: to reach a very high level in the squat or even more so in the competition lifts, you need to be able to train hard frequently and consistently. Which means avoiding injuries. I'm not talking about the odd injury that can happen top everybody, but if someone constantly get aches and pains whenever training is ramped up, then it is unlikely that this person will ever reach very high levels in strength.
Also, having the right structure for a lift helps. If you are born with longer legs and narrow hips, reaching very big squat number will always be much harder than if you are born with short legs and thick hips.
Then of course you have all those lifestyle thing like how many hours a week do your work; is your job mentally or physically draining, do you have a stressful life, do you get enough sleep, can you afford a lot of quality food, etc.
I think that the internet has done a disservice to most of use as far as establishing what is an achievable goal. With all the 700, 800, 900 and even 1000 squats video we now see, a 500lbs (227kg) squat seems "light" ... easily achievable. Well a true, full, high bar squat with 227kg is VERY good for someone in the low 200 of body weight. It is certainly not something that is achievable by everybody (if we are talking about a full range, regular stance, high bar, upright, squat).
So is it realistic to think about going from 106 to 227? What do YOU objectively think... considering what I mentioned earlier?
PERSONALLY I would say that in your situation it is NOT realistic. I wont say that it's impossible. But I would certainly put it somewhere in between "unlikely" and "impossible".