This paper deals with the crucial issue of random access (RA) preamble design and detection for 5G remote health systems based on satellite communication. In consideration of the characteristics of satellite environment and system compatibility, a long preamble sequence is first constructed by cascading multiple different root Zadoff-Chu (ZC) sequences with large subcarrier interval in time domain. Then, we further present a multiple sequence joint correlation (MSJC) based timing detection scheme to estimate the value of timing advance (TA) in one step. By flexibly adjusting the number of ZC sequences involved in correlation operation, the proposed method not only is capable of effective mitigation of noise, but also can achieve the robustness to large carrier frequency offsets (CFOs). Simulation results consist with mathematical analysis, and demonstrate that the proposed method significantly improves performance in terms of timing mean square error (MSE), compared with the previous methods.