The paper resolves the long-standing issue of the nature of the quantum phase transition between a Néel antiferromagnet and a spontaneously dimerized valence-bond solid in two-dimensional spin-1/2 magnets. 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. Using large-scale quantum Monte Carlo (QMC) calculations, they provide unambiguous evidence for first-order transitions in these models, with the strength of the discontinuities increasing with $n$. For the widely studied $n = 2$ and $n = 3$ models, 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 (critical exponents) that are common to models with small $n$, indicating close proximity to a universal quantum critical point. By combining two different $Q$ terms, specifically considering 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 $\beta \approx 0.85$. This exponent and others coincide closely with known rigorous bounds for an SO(5) symmetric conformal field theory (CFT), but in contrast to prevailing scenarios, 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 $\beta$ value and a large correlation length exponent, $\nu \approx 1.4$, 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, and interactions involving many spins are required to observe strong effects of the relevant SO(5) singlet. The results suggest that the multicritical point is likely the top of a gapless spin liquid phase recently discovered in frustrated Heisenberg models, into which the $J$-$Q$ models can be continuously deformed. The findings are at variance with the conventional scenario of generic deconfined quantum critical points, including the complex CFT proposal. The multicritical point should exist within real Hamiltonians, though perhaps only outside the regime amenable to sign-free QMC simulations.The paper resolves the long-standing issue of the nature of the quantum phase transition between a Néel antiferromagnet and a spontaneously dimerized valence-bond solid in two-dimensional spin-1/2 magnets. 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. Using large-scale quantum Monte Carlo (QMC) calculations, they provide unambiguous evidence for first-order transitions in these models, with the strength of the discontinuities increasing with $n$. For the widely studied $n = 2$ and $n = 3$ models, 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 (critical exponents) that are common to models with small $n$, indicating close proximity to a universal quantum critical point. By combining two different $Q$ terms, specifically considering 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 $\beta \approx 0.85$. This exponent and others coincide closely with known rigorous bounds for an SO(5) symmetric conformal field theory (CFT), but in contrast to prevailing scenarios, 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 $\beta$ value and a large correlation length exponent, $\nu \approx 1.4$, 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, and interactions involving many spins are required to observe strong effects of the relevant SO(5) singlet. The results suggest that the multicritical point is likely the top of a gapless spin liquid phase recently discovered in frustrated Heisenberg models, into which the $J$-$Q$ models can be continuously deformed. The findings are at variance with the conventional scenario of generic deconfined quantum critical points, including the complex CFT proposal. The multicritical point should exist within real Hamiltonians, though perhaps only outside the regime amenable to sign-free QMC simulations.