Given mean and SD, can we approximate the underlying distribution? I know the following info for values of a particular column for a dataset:
[mean=4.989209978967438, stddev=2255.654165352454, count=2400088]
Given just this, is it possible to approximate what the underlying distribution might be?
 A: Not unless you already know what the distribution is. And likely not even then, unless it's a normal or lognormal distribution (which can be completely described by those two values). 
You can calculation the mean and standard deviation from any set of numbers sampled from any distribution, so you cannot recreate a distribution based on them alone. 
They do contain some information, of course. Your summaries indicate that the distribution is either heavily skewed or allows negative values (or both). 

Edit: Since the distribution is skewed, it's definitely not a normal distribution, though it might be lognormal. 
h/t to @ChrisHaug for pointing out my oversight about the lognormal
A: You cannot conclude just from the first two moments what is the generating distribution. However, you can narrow the generating candidate distribution, depending on whether the number of observations is considered enough to converge to the Gaussian. If you assume, that your sample approximates the Gaussian, then you can say that the underlying distribution would belong in the family of alpha stable distributions with parameter $\alpha$ that allows the law of large numbers to work. Essentially, that describes the following work:
The Law of large numbers under fat tails by Nassim Taleb
Note however that you have some indicators of whether sample distribution approaches the Gaussian. Otherwise, you are blind
