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Locus of (x,y) which is at distance 5 from  C (-2,3) will be a circle with C as center and radius 5.
distance between P(x,y)  and C(-2,3) is
        SQUAREROOT [   (x+2)² + (y-3)²  ]  = 5
Now square on both sides (x+2)² + (y-3)² = 25            this is the answer
OR, we can expand the above :  x² +4x + y² -6y -12 = 0