  The global Langlands conjecture for $\text{GL}_n$ over a number field $F$
predicts a correspondence between certain algebraic automorphic representations
$\pi$ of $\text{GL}_n(\mathbb{A}_F)$ and certain families $\{ \rho_{\pi,\ell}
\}_\ell$ of $n$-dimensional $\ell$-adic Galois representations of
$\text{Gal}(\overline{F}/F)$. In general, it is expected that the image of the
residual Galois representations $\overline{\rho}_{\pi,\ell}$ of the
$\rho_{\pi,\ell}$'s should be as large as possible for almost all primes
$\ell$, unless there is an automorphic reason for it does not happen.
  In this paper, we study the images of certain compatible systems of Galois
representations $\{\rho_{\pi,\ell} \}_\ell$ associated to regular algebraic,
polarizable, cuspidal automorphic representations $\pi$ of
$\text{GL}_n(\mathbb{A}_F)$ by using only standard techniques and currently
available tools (e.g., Fontaine-Laffaille theory, Serre's modularity
conjecture, classification of the maximal subgroups of Lie type groups, and
known results about irreducibility of automorphic Galois representations and
Langlands functoriality). In particular, when $F$ is a totally real field and
$n$ is an odd prime number $\leq 393$, we prove that (under certain automorphic
conditions) the images of the residual representations
$\overline{\rho}_{\pi,\ell}$ are as large as possible for infinitely many
primes $\ell$. In fact, we prove the large image conjecture (i.e. large image
for almost all primes $\ell$) when $F=\mathbb{Q}$ and $n=5$.
