But this is where things stood in 80s, before dark energy in the late 90s. From page 18Yes, good point. And a density only 30% of critical (much less only 5% of critical) would not be anywhere close enough to critical for this.
"By 1983, inflation had become the driving force in cosmology because of the power of its three big predictions: (i) flat Universe (##\Omega_0=1##); (ii) almost scale-invariant spectrum of nearly-Gaussian density (curvature) perturbations;21 and (iii) almost scale-invariant spectrum of gravitational waves (134).
The first prediction made inflation both bold and falsifiable: the observational evidence at the time was ##\Omega_0 \sim 0.1##, and so there must be something in the Universe in addition to baryons"
The article at the link above is a detailed history of modern cosmology by one of giants, Mike Turner, and is technical but largely non-mathematical. I "discovered" it a couple of hours ago.