This paper presents unambiguous evidence for a line of first-order quantum phase transitions between a Néel antiferromagnet (AFM) and a spontaneously dimerized valence-bond solid (VBS) in two-dimensional spin-1/2 magnets, ending at a multicritical point with emergent SO(5) symmetry. Using large-scale quantum Monte Carlo (QMC) simulations, the authors study a class of J-Q models, where the standard Heisenberg exchange J competes with multi-spin interactions Q_n formed by products of n singlet projectors on adjacent parallel links of the lattice. They find that first-order transitions occur in these models, with the strength of the discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak but observable in correlation functions on large lattices. On intermediate length scales, they extract well-defined scaling dimensions that are common to the models with small n, indicating close proximity to a universal quantum critical point. By combining two different Q terms, specifically the J-Q_2-Q_6 model, the transition can be continuously tuned from weak to more strongly first-order. In the plane (Q_2, Q_6), with J=1-Q_2, the two coexisting order parameters on the first-order line scale with an unusually large exponent β ≈ 0.85. This exponent and others coincide closely with known rigorous bounds for an SO(5) symmetric conformal field theory (CFT), but the leading SO(5) singlet operator is relevant and responsible for the first-order transition ending at a fine-tuned multicritical point. The authors quantitatively characterize the emergent SO(5) symmetry by computing the scaling dimensions of its leading irrelevant perturbations. The large β value and a large correlation length exponent, ν ≈ 1.4, partially explain why the transition remains near-critical on the first-order line even quite far away from the critical point and in many different models without fine-tuning. They also find that few-spin lattice operators are dominated by their content of the SO(5) violating field (the traceless symmetric tensor), and interactions involving many spins are required to observe strong effects of the relevant SO(5) singlet that brings the system into the coexistence line. Beyond the scaling dimensions that can be directly explained by the CFT, the exponent that had previously been identified with the divergent correlation length when crossing between the two phases does not have a corresponding level in the CFT spectrum. The authors explain this emergent "pseudocritical" length scale by a mechanism relying on a dangerously irrelevant SO(5) perturbation in combination with repulsive interactions between the two order parameters. This length scale is reflected in crossover behaviors of observables when traversing the weak first-order line. The authors argue that the multicritical point is also most likely the top of a gapless spinThis paper presents unambiguous evidence for a line of first-order quantum phase transitions between a Néel antiferromagnet (AFM) and a spontaneously dimerized valence-bond solid (VBS) in two-dimensional spin-1/2 magnets, ending at a multicritical point with emergent SO(5) symmetry. Using large-scale quantum Monte Carlo (QMC) simulations, the authors study a class of J-Q models, where the standard Heisenberg exchange J competes with multi-spin interactions Q_n formed by products of n singlet projectors on adjacent parallel links of the lattice. They find that first-order transitions occur in these models, with the strength of the discontinuities increasing with n. For n=2 and n=3, the first-order signatures are very weak but observable in correlation functions on large lattices. On intermediate length scales, they extract well-defined scaling dimensions that are common to the models with small n, indicating close proximity to a universal quantum critical point. By combining two different Q terms, specifically the J-Q_2-Q_6 model, the transition can be continuously tuned from weak to more strongly first-order. In the plane (Q_2, Q_6), with J=1-Q_2, the two coexisting order parameters on the first-order line scale with an unusually large exponent β ≈ 0.85. This exponent and others coincide closely with known rigorous bounds for an SO(5) symmetric conformal field theory (CFT), but the leading SO(5) singlet operator is relevant and responsible for the first-order transition ending at a fine-tuned multicritical point. The authors quantitatively characterize the emergent SO(5) symmetry by computing the scaling dimensions of its leading irrelevant perturbations. The large β value and a large correlation length exponent, ν ≈ 1.4, partially explain why the transition remains near-critical on the first-order line even quite far away from the critical point and in many different models without fine-tuning. They also find that few-spin lattice operators are dominated by their content of the SO(5) violating field (the traceless symmetric tensor), and interactions involving many spins are required to observe strong effects of the relevant SO(5) singlet that brings the system into the coexistence line. Beyond the scaling dimensions that can be directly explained by the CFT, the exponent that had previously been identified with the divergent correlation length when crossing between the two phases does not have a corresponding level in the CFT spectrum. The authors explain this emergent "pseudocritical" length scale by a mechanism relying on a dangerously irrelevant SO(5) perturbation in combination with repulsive interactions between the two order parameters. This length scale is reflected in crossover behaviors of observables when traversing the weak first-order line. The authors argue that the multicritical point is also most likely the top of a gapless spin