Answer
Domain = $\mathbb{R}\backslash\{-1,-4\}$ or
$\{t\in \mathbb{R}\ \ |\ t\neq-1, t\neq-4\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined (for which f(x) can be calculated).
Factoring the denominator, we search for factors of 4 that add to 5,
... they are 1 and 4.
$f(t)=\displaystyle \frac{1}{(t+1)(t+4)}$
can be calculated for any real $t$, except $t=-1$ and $t=-4$,
which yield zero in the denominator.
Domain = $\mathbb{R}\backslash\{-1,-4\}$ or $\{t\in \mathbb{R}\ \ |\ t\neq-1, t\neq-4\}$
