  We calculate the electro- and chromomagnetic dipole coefficients
$C_{7\gamma,8g}$ and $\tilde C_{7\gamma,8g}$ in the context of the minimal
Randall-Sundrum (RS) model with a Higgs sector localized on the IR brane using
the five-dimensional (5D) approach, where the coefficients are expressed in
terms of integrals over 5D propagators. Since we keep the full dependence on
the Yukawa matrices, the integral expressions are formally valid to all orders
in $v^2/M_{\rm KK}^2$. In addition we relate our results to the expressions
obtained in the Kaluza-Klein (KK) decomposed theory and show the consistency in
both pictures analytically and numerically, which presents a non-trivial
cross-check. In Feynman-'t Hooft gauge, the dominant corrections from virtual
KK modes arise from the scalar parts of the $W^\pm$-boson penguin diagrams,
including the contributions from the scalar component of the 5D gauge-boson
field and from the charged Goldstone bosons in the Higgs sector. The size of
the KK corrections depends on the parameter $y_\ast$, which sets the upper
bound for the anarchic 5D Yukawa matrices. We find that for $y_\ast\gtrsim1$
the dominant KK corrections are proportional to $y_\ast^2$. We discuss the
phenomenological implications of our results for the branching ratio ${\rm
Br}(\bar B\to X_s\gamma)$, the time-dependent CP asymmetry $S_{K^*\gamma}$, the
direct CP asymmetry $A_{\rm CP}^{b\to s\gamma}$ and the CP asymmetry difference
$\Delta A_{\rm CP}^{b\to s\gamma}$. We can derive a lower bound on the first KK
gluon resonance of $3.8\,$TeV for $y_\ast=3$, requiring that at least $10\%$ of
the RS parameter space covers the experimental $2\sigma$ error margins. We
further discuss the branching ratio ${\rm Br}(\bar B\to X_sl^+l^-)$ and compare
our predictions for $C_{7\gamma,9,10}$ and $\tilde C_{7\gamma,9,10}$ with
phenomenological results derived from model-independent analyses.
