We use a radio-frequency (RF) diode laser modulation technique to interrogate a fiber Fabry-Perot (FFP), and demonstrate unprecedented remote sensitivity performance for measuring fiber dynamic strain. We present results for its experimental demonstration in a 5 km remote strain sensing system, where we have attained sub-picostrain/√Hz resolution in an acoustic signal band from 100 Hz to 100 kHz, with better than 300 femtostrain/√Hz sensitivity above 300 Hz. This is unprecedented in sensitivity and broadband performance, unparalleled over such a long interrogation distance. Strain signals are extracted interferometrically from the differential phase between the carrier and its RF sidebands. This elegant architecture is immune to intensity noise in the laser, as well as ambient acoustic and mechanical perturbations in the remote delivery fiber. The excellent frequency discrimination by the FFP also facilitates a superior signal-to-noise ratio, to effectively overcome the random phase noise due to Rayleigh backscatter in the long length of fiber. Furthermore, the interrogation length can be well beyond the coherence length of the laser source. We show that this performance is limited only by the frequency noise of the diode laser source, as all systemic noise sources in the delivery fiber are effectively transparent to the sensing architecture. This remote sensitivity is a seminal demonstration for a range of applications, such as sea floor acoustic sensing arrays, deep sea hydrophone arrays, and remote surveillance. We will discuss upscaling of this single element experiment to multi-element sensing arrays.