Solution:-
Let the number to be added be A
Now,

Transposing (−5x³+ 4x − 3 ) to other side-

Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket

Putting like terms together -


Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1