Yes.I assume this is compromised structurally?
That depends. What else has been corroding? Regarding the mast, you can pull it from the boat, cut the cancer section off, and attach a replacement piece. (The height of the mast is critical for the sails you have and the wire rigging holding the mast in place. That would all have to be changed if you just cut the cancer portion out.)Cut it, replace it, don’t sail it, scuttle the boat?
If the corrosion is just 5" up, I'd do what is described above. Your base plate structure is also highly corroded and about to fail, so you need a new mast base anyway. Cut off that 5" and fab up an elevated platform with a new base mount. It puts the foot of the mast out of the bilge, and you don't have to refit the rigging/boom/sails. There won't be any issues or complications with this change, and any forces will stay as original.Given the location of the pitting in the picture, if the affected area doesn’t go up too far I don’t hate the idea of cutting the mast and building a new elevated platform under it to preserve the mast height.