Concept: Ascending order by birth year means arranging the thinkers from the earliest born to the latest born.
Step 1: Write the birth years.
F.W. Taylor was born in 1856.
\[
A = 1856
\]
Henry L. Gantt was born in 1861.
\[
B = 1861
\]
Max Weber was born in 1864.
\[
C = 1864
\]
Mary Parker Follett was born in 1868.
\[
E = 1868
\]
Elton Mayo was born in 1880.
\[
D = 1880
\]
Step 2: Arrange from earliest to latest.
\[
1856 < 1861 < 1864 < 1868 < 1880
\]
Step 3: Convert into letters.
\[
A,\ B,\ C,\ E,\ D
\]
Therefore, the correct answer is option (C).