The Hubble Space Telescope Fine Guidance Sensors data on 23 stars in the intermediate-age cluster M35 having B-V<0.5 (~F7V) are analyzed to test whether binary periods, separations, and masses can be estimated by measuring periodic variations in the residuals of their internal proper motions. Of the 23 stars examined, 4 appear to possess a periodic signal. Unfortunately, these detections cannot be considered firm because the amplitudes of these waveforms are small (~1mas), the signal is only seen in one coordinate, and the derived periods are close to the duration of the data set. If the signals are real, they predict binary separations of >6AU, secondary masses between 0.3 and 0.6M_{sun}_, and mass ratios of about 0.2. This latter value is in agreement with capture models employing stars with circumstellar disks for the formation of binaries.