The authors compute the 5PM order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order (1SF) using the worldline quantum field theory (WQFT) formalism. This challenging four-loop computation required advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Partial fraction identities were used to simplify the integrand into a fully planar form, resulting in a function space simpler than expected: multiple polylogarithms up to weight three, without elliptic integrals appearing as in the 4PM order. All checks on the results, both internal and external, were passed, including cancellation of dimensional regularization poles, preservation of the on-shell condition, and matching with post-Newtonian (PN) literature up to 5PN order and tail terms with the 4PM loss of energy. The computation is motivated by the need for high precision in gravitational waveforms from binary black hole and neutron star mergers, which are routinely observed by LIGO-Virgo-KAGRA and will be further enhanced by upcoming gravitational wave detectors and LISA. The 5PM-1SF momentum impulse is decomposed into basis functions and coefficient polynomials, with the final result agreeing with the 5PM-0SF order scattering angle from previous work.The authors compute the 5PM order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order (1SF) using the worldline quantum field theory (WQFT) formalism. This challenging four-loop computation required advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Partial fraction identities were used to simplify the integrand into a fully planar form, resulting in a function space simpler than expected: multiple polylogarithms up to weight three, without elliptic integrals appearing as in the 4PM order. All checks on the results, both internal and external, were passed, including cancellation of dimensional regularization poles, preservation of the on-shell condition, and matching with post-Newtonian (PN) literature up to 5PN order and tail terms with the 4PM loss of energy. The computation is motivated by the need for high precision in gravitational waveforms from binary black hole and neutron star mergers, which are routinely observed by LIGO-Virgo-KAGRA and will be further enhanced by upcoming gravitational wave detectors and LISA. The 5PM-1SF momentum impulse is decomposed into basis functions and coefficient polynomials, with the final result agreeing with the 5PM-0SF order scattering angle from previous work.