I assume you're dividing t+5 into 5t4-10t2+6: (algebraic long division)
5t3 -25t2+115t -575 (quotient)
t+5 ) 5t4 -10t2 +6
5t4+25t3 (subtract)
-25t3 -10t2
-25t3-125t2 (subtract)
115t2 +6
115t2+575t (subtract)
-575t +6
-575t-2875 (subtract)
2881 (remainder)