Under investigation in this paper is a nonisospectral and variable-coefficient fifth order Korteweg-de Vries equation in fluids. By virtue of the Bell polynomials and symbolic computation, the bilinear form, Backlund transformation and Lax pair are obtained. Based on its bilinear form, N-soliton solutions are constructed. Furthermore, periodic wave and breather wave solutions are obtained by virtue of the Riemann theta function and homoclinic test approach, respectively. In addition, the characteristic-line method is applied to discuss the features of the solitons for the nonisospectral problem, such as the amplitude, velocity and width of the solitary wave. (C) 2016 Elsevier Ltd. All rights reserved.