Instead of quoting any particular post, I figure I should start clean here:
What some of us are trying to explain is that the dynamic range of what you are trying to do is way too high.
Let's start with the shunt resistor.
Let's assume at the bottom of your range you're willing to accept a 1uV input from your shunt. This is probably way too low to be useful, but let's go there anyways. Getting 1uV at 1uA takes a 1
resistor. At this end of the range the power dissipated by the resistor is negligible. 1e-8 watts.
Now, let's go to the other end of your range. Putting 5A through that same 1
resistor will now result in a 5V drop (burden voltage), and 25W of power dissipation. That much power being dissipated in the shunt resistor is going to cause serious heating and will cause serious drift just due to the temperature coefficient of the resistor. Not to mention that I'm not even sure you can get a 25W resistor with good enough accuracy/tempco effects (someone will probably let me know of some esoteric part which does).
Let's move on from the shunt.
Let's say that you instead just want to be able to measure from 1uV to 5V. This is 5,000,000 counts, aka 7.5 digits. In the ADC world, this does require somewhere between 22 and 23 bits of accuracy. 24 bits will give you some reasonable room to move. One would think you could just slap a 24 bit adc on there and it would work fine. But if this were the case, you'd have rigol and the like selling 7.5 digit dmm's for $99.00. There's a reason that even the least expensive reasonable quality 5.5 digit DMM's cost multiple times that.
The real challenge is that electronics are really not that stable. We've all been programmed to believe so with modern electronic design, but underneath it all, things drift, things aren't as accurate as you'd like. Everything is affected by temperature. At the lowest voltages even the temperature gradients on the circuit boards matter since the resistance of the traces change causing voltage offsets. And on and on. Getting a 7.5 digit anything done takes a lot of work and a lot of patience. There's a reason why the 7.5 digit DMM's are well over a thousand dollars, even when bought used.
The real killer is dynamic range. Although it is definitely quite difficult to read down to 1uV, it is even harder to read both 1uV and 5V without a range switch. Most electronics like their signal to be bounded in a tight little range. This is any thing but tight. So you get to not only deal with the challenges of dealing with voltages down at the microvolt level, but you also have to deal with the challenges of high dynamic range, which is another challenge at least as difficult as the "micro voltage" issues.
I agree with others that a high precision project like this is an interesting thing for a beginner. But be aware that a project like this takes a *lot* of attention to detail, and a lot of frustration, and a lot of research and most importantly a lot of experimentation and learning. You may find that it is even impossible as stated, and so your goal may have to change, or even be abandoned. As long as you are treating this as a project you may never finish but instead learn from the journey, then I'd say go for it. But please be aware that every problem solved will likely make you discover a new problem. And another and another. But each of these is a learning experience.
P.S. I'm a big fan of nearly impossible goals, as it tends to prevent you from reaching a goal and then quitting. The trick is understanding how to gain satisfaction from each step, instead of from reaching the goal. And if by chance you get to what you thought was an nearly impossible goal, by all means pick another and proceed on.