Hypergeometric Distribution-Cards Suppose we select 5 cards. What is the probability of getting two or fewer hearts?
N=the number of items in the population 
m= the number classified as success in the population
n= the number of items in the sample
x=the number of items in the sample classified as success
When finding the values I came up with:
$N=52$
$n=5$
$x=2$
$m=13$
I found this  was incorrect as I solved for $m-n\choose n-x$ I got negative values for $n-x$ and $n-m$

You should not be getting negative terms in the binomials coefficients using: $N= 52,\\ M=13,\\ n=5,\\ x\in\{0,1,2\}$
$$\begin{align}\mathsf P(X\leq 2) &= \sum\limits_{x=0}^2 \left.\dbinom {M}{x}\dbinom{N-M}{n-x}\middle/ \dbinom{N}{n}\right. \\[1ex] & = \dfrac{\dbinom{13}{0}\dbinom{52-13}{5-0}+\dbinom{13}{1}\dbinom{52-13}{5-1}+\dbinom{13}{2}\dbinom{52-13}{5-2}}{\dbinom{52}5} \end{align}$$
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