  By inferring the dynamic permittivity of different material media from the
observations and calculating dynamic electric dipole polarizabilties of the Li
through Cs alkali atoms, precise values of $C_3$ coefficients were estimated in
Phys. Rev. A {\bf 89}, 022511 (2014) and Phys. Lett. A {\bf 380}, 3366 (2016).
Since significant contribution towards the long range van der Waals potential
is given by the quadrupole polarization effects, we have estimated the $C_5$
coefficients in this work arising from the quadrupole polarization effects of
all the alkali atoms interacting with metal (Au), semiconductor (Si) and four
dielectric materials (SiO$_2$, SiN$_x$, YAG and sapphire). The required dynamic
electric quadrupole (E2) polarizabilities are evaluated by calculating E2
matrix elements of a large number of transitions in the alkali atoms by
employing a relativistic coupled-cluster method. Our finding shows that
contributions from the $C_5$ coefficients to the atom-wall interaction
potentials are pronounced at short distances (1$-$10 nm). The $C_3$
coefficients of Fr atom interacting with the above material media are also
reported. These results can be useful in understanding the interactions of
alkali atoms trapped in different material bodies during the high-precision
measurements.
