We have obtained deep photometry in two 1 ^ { \circ } \times 1 ^ { \circ } fields covering the close pair of dwarf spheroidal galaxies Leo IV and Leo V and part of the area in between . From the distribution of likely red giant branch and horizontal branch stars in the data set , we find that both Leo IV and Leo V are significantly larger than indicated by previous measurements based on shallower data . With a half-light radius of r _ { h } =4 \farcm 6 \pm 0 \farcm 8 ( 206 \pm 36 pc ) and r _ { h } =2 \farcm 6 \pm 0 \farcm 6 ( 133 \pm 31 pc ) , respectively , both systems are now well within the physical size bracket of typical dwarf spheroidal Milky Way satellites . Both are also found to be significantly elongated with an ellipticity of \epsilon \simeq 0.5 , a characteristic shared by many of the fainter ( M _ { V } > -8 ) Milky Way dwarf spheroidals . The large spatial extent of our survey allows us to search for extra-tidal features in the area between the two dwarf galaxies with unprecedented sensitivity . The spatial distribution of candidate red giant branch and horizontal branch stars in this region is found to be non-uniform at the \sim 3 \sigma level . Interestingly , this substructure is aligned along the direction connecting the two systems , indicative of a possible ‘ bridge ’ of extra-tidal material . Fitting the stellar distribution with a linear Gaussian model yields a significance of 4 \sigma for this overdensity , a most likely FWHM of \sim 16 arcmin and a central surface brightness of \simeq 32 mag arcsec ^ { -2 } . We investigate different scenarios to explain the close proximity of Leo IV and Leo V and the possible tidal bridge between them . Orbit calculations demonstrate that the two systems can not share the exact same orbit , while a compromise orbit does not approach the Galactic center more than \sim 160 kpc , rendering it unlikely that they are remnants of a single disrupted progenitor . A comparison with cosmological simulations shows that a chance collision between unrelated subhalos is negligibly small . Given their relative distance and velocity , Leo IV and Leo V could be a bound ‘ tumbling pair ’ , if their combined mass exceeds 8 \pm 4 \times 10 ^ { 9 } M _ { \sun } . The scenario of an internally interacting pair that fell into the Milky Way together appears to be the most viable explanation for this close celestial companionship .