RFe₅Al₇ (R - Gd, Tb, Dy, Ho, Er and Tm) single crystals have been studied by measurements of magnetization, sound propagation (in static and pulsed magnetic fields up to 60 T) and specific heat. Fundamental magnetic properties have been determined and compared for all these materials. RFe₅Al₇ are highly anisotropic ferrimagnets. Spontaneous and field-induced magnetic phase transitions of anisotropic and exchange nature have been observed in RFe₅Al₇. Strong magnetoelastic interactions are manifested by pronounced acoustic anomalies at the phase transformations. The detected magnetization jumps provide important information on the R-Fe inter-sublattice exchange interactions.