You've got it right. The experimental unit is whatever the treatment was randomised onto, and you randomised onto plots. So you have 5 true replicates per treatment, 20 experimental units in total. Plants within a plot, and shoots within a plant, are subsamples rather than replicates. Treating plants as independent is textbook pseudoreplication -- it would shrink your standard errors by roughly sqrt(5) and inflate your Type I error to match.

Two defensible ways to analyse it. The simple one is to average to the plot and run the RCBD analysis on those 20 numbers, treatment plus block. With equal plant numbers per plot and no missing data that gives you essentially the same test of treatment as anything fancier.

The other is to keep the hierarchy in a mixed model, something like

lmer(ripening ~ treatment + (1|block) + (1|block:plot) + (1|block:plot:plant))

which loses no information and additionally tells you how the variance partitions across plot, plant and shoot levels. That part is genuinely useful for designing the next trial: if most of the variance sits between plants rather than between plots, more plots beats more plants per plot. The treatment F test here uses plot-within-block as its error term, which is the same denominator the averaged analysis is using implicitly.

For references, Gomez & Gomez, Statistical Procedures for Agricultural Research, is the standard field-trial text and is explicit about the plot being the unit when treatments are applied to plots. Hurlbert 1984, "Pseudoreplication and the design of ecological field experiments" (Ecological Monographs 54:187-211), is the canonical citation for why subsamples aren't replicates. If you want the model algebra for the subsampling case worked through, Milliken & Johnson's Analysis of Messy Data vol. 1 covers it.