Will changing the standard deviation affect the distribution? Let's say I want to generate some random data that follows the normal distribution, with a mean of 5. Will setting the standard deviation to 3 or 5 affect the distribution, that is,  will it still follow the normal distribution?
I am confused on this question because the data's mean and variance are based on the data, and there are specific way of calculating them for different distribution. 
*edit for clarification:
I want to generate TWO data sets: both of them follow the normal distribution with a mean of 5. The 1st data set has $\mu =5$ AND $\sigma= 5 $. If I generate the 2nd data set by changing the $\sigma$ from 5 $\rightarrow$3, will the data still follow the normal distribution. 
 A: If you take one data sample $\{X_i\}_{i=1}^{100} \sim \mathcal N(5, 5^2)$, that is, $X_1$ through $X_{100}$ each following a normal distribution with mean and standard deviation $5$ – and then a different data sample $\{Y_i\}_{i=1}^{100} \sim \mathcal N(5, 3^3)$, then:
$X$ and $Y$ each still follow a normal distribution. They don't affect each other in any way.
If you combine the two datasets together, they don't follow a normal distribution anymore; instead, they follow a mixture of Gaussians. You can find the mean and find the variance of this mixture pretty easily with a very small amount of math. This is what quester's answer does empirically.
A: for example if I will generate 6 observations from $N(5, 3)$ and 4 from $N(5, 5)$ all 10 observations should be considered to follow distribution $N(5, 3^2*\frac{6}{10} + 5^2*\frac{4}{10}) = N(5,15.6)$
so in general data as a whole will follow mixture of normal distributions but with variance being weighted sum of variances of original distributions
