Using the quasilinearized formulation of CC theory in terms of recursively computed intermediates, we present the detailed equations and implementation of coupled-cluster theory with single, double, triple, quadruple, and pentuple excitations, CCSDTQP. We illustrate its results by comparison with several full CI results in double zeta, polarized basis sets (DZP), at different geometries. The maximum error compared to full CI occurs for H2O at twice R-e which is 0.026 mH. For all other cases, HF, SiH2, and CH2 in its singlet state, the largest errors are 0.001 mH. The magnitude of the connected T-5 contribution is as large as 0.35 mH, but usually less than 0.1 mH for these examples.