Twenty four hours after clinching stage four, the Giant-Shimano rider repeated that feat at the end of the 80km route between Priego de Cordoba and Ronda.
Orica GreenEDGE's Michael Matthews remains at the top of the overall classification as he extended his lead over Movistar's Nairo Quintana to 13 seconds.
Degenkolb narrowly prevailed in a thrilling finish to a stage that saw the lead change hands a number of times in the final kilometre.
The German was able to just get the better of FDJ.fr's Bouhanni, who attempted to overtake his rival on the inside on the final straight, and appeared to raise his arms in protest at Degenkolb's sprinting line.
Matthews ended the stage 11th, while a late split in the peloton means Quintana and his fellow Movistar rider Alejandro Valverde lost ground on the Australian.
Caja Rural's Luis Mas Bonet remains atop the mountain classification after clinching a point on Wednesday, while his team-mate Amets Txurruka took the maximum three on offer and is now four behind his compatriot overall.
In the overall points standings, Degenkolb's back-to-back victories mean he is at the summit on 70, with Bouhanni his nearest challenger on 54 and Matthews a further nine behind in third.
On Thursday, the riders will take on stage six - a 167.1km stint between Benalmadena and La Zubia.