Why do most carboxylic acids have high pKa (~5) in spite of having a conjugate base ion that is stabilized by resonance?
Everything is relative in acid-base reactions; the equilibrium will favor the side with the weaker acid. A carboxylic acid with $\ce{pKa = 5}$ will not protonate $\ce{H2O}$ significantly because $\ce{pKa(H3O+) = -0.7}$, but it will protonate something more basic like $\ce{NH3}$ because $\ce{pKa(NH4+) = 9.24}$.

Note: the pKa of $\ce{H3O+}$ is debated, see What is the pKa of the hydronium, or oxonium, ion (H3O+)? for more discussion.