Yes, you can install a Diaphragm pump c/w strainer on suction hose. Jabsco (Par) makes several, including the small #30705 rated @ 3.8 GPM Open, and the larger #34600 rated 10.8 GPM. Flojet makes a 5 GPM unit, the #4125. Others by Groco.
All have good websites for info''.
BTW: You indicate a ''deep'' bilge, but only 5 Ft of head (lift actually, total head will be more due to friction losses) - so sounds like your discharge thruhull is not all that high above W/L.