Why doesn't this set have a supremum in a non-complete field?

Why doesn't this set have a supremum in a non-complete field?

Why doesn't the set $\{x:x^2<5\}$ have a supremum in $\mathbb{Q}$? I know
that the rational numbers aren't a complete field, but I'm still not
understanding how a set can have upper bounds, but no least upper bound in
a field.
In $\mathbb{Z}$ for example, $\{x:x^2<5\}=\{-2,-1,0,1,2\}$. It has the set
of upper bounds: $[2,\infty)\cup\mathbb{Z}$. So why isn't the least upper
bound $2$?