Hello, stats question please. Confidence intervals.

Let's say I have 5,000 daily values in a time series, and that the sample standard deviation of those 5,000 values is 10, with a mean of, say, 0.

I would say that, with 90% confidence, the next day's value will be between -10 and 10, right?

But I had this discussion with someone who says that you need to divide the SD by sqrt(5000-1), -> (-.14, .14)

I of course know the formula that they are using, but I forget why and when that's used, seems retarded here. What's going on? pic is dog