On massive higher spins and gravity. I. Spin 5/2

In this paper, we continue our investigation of gravitational interactions for massive higher spins extending our previous work on massive spin 3/2 and spin 2 to massive spin 5/2, including partially massless and massless limits. We use the gauge invariant frame-like description for massive fields, both for general analysis of possible vertices and for constructing the minimal vertex (i.e. vertex containing standard minimal interactions and non-minimal interactions with a minimum number of derivatives). In particular, we show that there is a special point m^2 = 4\Lambda, which corresponds to the boundary of a unitary allowed region in dS_4, where minimal interactions disappear, leaving only non-minimal ones.