  Supposing the existence of modified Chaplygin gas with the equation of state
$p=A\rho-B/\rho^\beta$ as a cosmic background, we obtain a static
spherically-symmetric black hole solution to the Einstein-Gauss-Bonnet
gravitational equations in 5D spacetime. The spacetime structure of the
obtained black hole solution is analyzed, also the related black hole
properties are studied by calculating the thermodynamical quantities. During
this process, effects of the Gauss-Bonnet coupling constant and the modified
Chaplygin gas parameters on black hole solution, as well as on its
thermodynamical properties are discussed. At the end, we study the quantum
tunneling of scalar particles and the propagating of scalar waves within the
background of modified Chaplygin gas. The study shows that the system is stable
under scalar perturbations and the Hawking radiation could stop at some point,
leaving an extremal black hole as remnant for evaporation.
