Taylor Polynomial of degree 5 centered around x=x I was wondering if this was possible. For a taylor series polynomial shouldn't it be centered around $x_0$ instead of $x$?

The question was asking for a Taylor polynomial of degree five in the form of $f(x+h,y)$ in $x+h$ centered around $x$, keeping $y$ as a constant, so I wrote something like:

$$f(x+h)\approx\sum_{n=0}^{5}\frac{f^{(n)}(x)}{n!}(x+h)^n$$

But I think it should be something like this:

$$f(x+h)\approx\sum_{n=0}^{5}\frac{f^{(n)}(h)}{n!}(x+h)^n$$

Is this correct or am I missing something?
The idea is to treat $x+h$ as a variable.  Let's let $z=x+h$. Now

$$f(z,y)\approx\sum_{n=0}^5\frac{f^{(n)}(x,y)}{n!}(z-x)^n=\sum_{n=0}^5\frac{f^{(n)}(x,y)}{n!}h^n.$$

The last expression comes from substituting $x+h$ for $z$.
The idea is to treat $x+h$ as a variable.  Let's let $z=x+h$. Now

$$f(z,y)\approx\sum_{n=0}^5\frac{f^{(n)}(x,y)}{n!}(z-x)^n=\sum_{n=0}^5\frac{f^{(n)}(x,y)}{n!}h^n.$$

The last expression comes from substituting $x+h$ for $z$.