The hyperactivity of the cyclic dependent kinase 5 (CDK5) induced by the activator protein p25 has been linked to a number of pathologies of the brain. The CDK5-p25 complex has thus emerged as a major therapeutic target for Alzheimer's disease (AD) and other neurodegenerative conditions. Experiments have shown that the peptide p5 reduces the CDK5-p25 activity without affecting the endogenous CDK5-p35 activity, whereas the peptide TFP5, obtained from p5, elicits similar inhibition, crosses the blood-brain barrier, and exhibits behavioral rescue of AD mice models with no toxic side effects. The molecular basis of the kinase inhibition is not currently known, and is here investigated by computer simulations. It is shown that p5 binds the kinase at the same CDK5/p25 and CDK5/p35 interfaces, and is thus a non-selective competitor of both activators, in agreement with available experimental data in vitro. Binding of p5 is enthalpically driven with an affinity estimated in the low µM range. A quantitative description of the binding site and pharmacophore is presented, and options are discussed to increase the binding affinity and selectivity in the design of drug-like compounds against AD.