The concept of action plays a central role in gravitational theories. In this work we introduced a surface term, which as the quintic quasitopological action has no well-defined variational principle, causes that for a spacetime with flat boundaries have a well-defined variational principle. To this end, nine terms of order nine in extrinsic curvature of the boundary have been introduced. The coefficients are chosen such that the normal variation of the metric to the flat boundary is canceled. This surface term can be employed in Hamiltonian formalism as well.Also we found the counterterm which removes non-logarithmic divergences for the static quintic quasitopological gravity. Using this counterterm one can calculate a finite action and conserved quantities for the quintic quasitopological gravity.Moreover, we investigated the numerical solutions of the above-mentioned gravity coupled to the nonlinear logarithmic and exponential electrodynamics. These nonlinear theories have the property that they are not divergent at the origin which is the generic problem for the linear Maxwell theory that is the limitation of this theory as β → ∞. Also it has no horizon and curvature except one conical singularity at r = 0 with a deficit angle δφ. This deficit angle does not depend on μ2 , μ3 , μ4 and μ5 coefficients but only on the parameters q, β and dimension n.