dice probability 2 dice are the same in 5

I have 5 dice that I roll. I want to find that at least 2 values are the same and at least 3 values are the same.

So for k=2: $P(2) = 1-P(\text{all values distinct}) = 1-\frac{6*5*4*3*2}{6^5}$ but for k=3 I thought it's $P(3)= P(2)-P(\text{exactly 2 values are the same})$ where $P(\text{exactly 2 values are the same}) = 6*\binom{5}{2}* (1/6)^2 *(5/6)^3$ but I get $P(3)$ negative... can you please help?

You are correct in that $P(X\ge3)=P(X\ge2)-P(X=2)$, but you have not correctly calculated $P(X=2)$

Having two values the same can be either one or two pairs.

Number of ways to make one pair is $6\times\binom{5}{2}\times5\times4\times3=3600$

Number of ways to make two pairs is $\binom{6}{2}\times\binom{5}{2}\times\binom{3}{2}\times4=1800$

Taken together, $P(X=2)=\frac{5400}{7776}$

Now, with $P(X\ge2)=\frac{7056}{7776}$ we have $P(X\ge3)=\frac{7056-5400}{7776}=\frac{1656}{7776}$