"So 1 in 11.2 chances of 1 particular number being chosen,"
That's fine for whether or not a particular number will be selected in any given drawing, but you're looking for the chances that any of the 5 numbers from a drawing will repeat in the next drawing. Here's how that works.
5 of the 56 numbers were in the last drawing and 51 of 56 were not. When the first number is selected there's a 51/56 chance it will not be any of the 5. If that happens there will be 55 numbers remaining, of which 50 were not selected in the previous drawing. That means there's a 50/55 chance of selecting anothe rnumber that's not a repeat. For the 3rd number it will be 49/54, then 48/53 for the 4th and 47/52 for the 5th number. Overall that means there's a 51/56 * 50/55 * 49/54 * 48/53 * 47/52 chance that none of the previous numbers will be repeated. Doing the math we get .615, or a 61.5% chance that none of the previous numbers will be repeated. Subtracting from 100% that leaves a 38.5% chance that 1 or more of the numbers will repeat. Note that that figure matches the history you looked at much more closely than the 44% figure.
So what does that do to help you out? Well, you could play all 5 numbers from the previous drawing and have a 38.5% chance of getting at least one number right. As a practical matter, almost all of that 38.5% is the chance of getting only 1 of the numbers right. How much do you win for doing that?
Still, let's pretend that there's actually an advantage to using numbers from the previous drawing. The advantage you'd get would only happen the 38.5% of the time that a number(s) does repeat. The other 61.5% of the time you'd lose that advantage. The theoretical advantage only happens some of the time, and is offset by the chance that there won't be repeats.
For a simple comparison consider playing 2 odd and 3 even numbers or 3 odd and 2 even numbers.Most of the possible combinations fit into one of those two patterns, so most of the winning combinatins fit one of those two patterns. That makes you more likely to have the winning combination if the winning numbers fit one of those patterns. If you have the right "patern" but not the right numbers you win nothing, so there's no advantage to that. If the winning numbers aren't one of those patterns, then you can't possibly have chosen the winning combination and you've got a 0.0% chance of winning.
In short, all you're doing is recreational math to calculate the odds for when a particular what if happens. Most of the time it's a different what if that happens. The only way to figure the odds for the real world, where you don't know which what if will happen, is to use the odds that include all of the what if's. Those are the odds that RJ gave you.