(2x-1)5 has 5+1 or 6 terms.

Construct Pascal's triangle down to the 6th line,
the one that starts "1   5".  Each line starts and
ends with 1 and every number is gotten by adding
two adjacent numbers to get the number between and
below.  For instance the 2 in the third line is
gotten by adding the two 1's above it and on each
side of it. The 3 on the 4th line is gotten by
adding the 1 and 2 just above it.

          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4   1    
1   5  10  10   5   1  

That 6 numbers on the bottom line are the "binomial 
coefficients" of the 6 terms.  Incidentally, they are 
also the combinations of 5 things taken 0 through 5 at 
a time.

Notice below the pattern of exponents of the two terms 
(2x) and (-1) carefully how one starts at 5 and goes 
down to 0 and the other starts and 0 and goes up to 5:

1(2x)5(-1)0+5(2x)4(-1)1+10(2x)3(-1)2+10(2x)2(-1)3+5(2x)1(-1)4+1(2x)0(-1)5

Simplify those 6 terms by using ordinary rules of exponents
and multiplication of algebra, remembering that (-1) raised to
an even power is +1 and when raised to an odd power is -1 which
makes the signs alternate between + to -:

32x5-80x4+80x3-40x2+10x-1

Edwin