EDIT1: If need convert list of strings to list of floats:
#change sample data
df = pd.DataFrame({'col1': [['-0.8783137', '0.05478287', '-0.08827557', '0.69203985', '0.06209986'],
['0.31444644', '-0.6546649', '0.7211526', '0.9819127', '0.74042267']]})
#dtype of lists is object
#https://stackoverflow.com/a/42672574/2901002
print (df['col1'].dtype)
object
#first value of column col1
print (df.loc[0, 'col1'])
['-0.8783137', '0.05478287', '-0.08827557', '0.69203985', '0.06209986']
#type of first value of column col1 is list
print (type(df.loc[0, 'col1']))
<class 'list'>
#first value of column col1 and first value of list
print (df.loc[0, 'col1'][0])
-0.8783137
#first value of column col1 and type of first value of list
print (type(df.loc[0, 'col1'][0]))
<class 'str'>
df['col1'] = df['col1'].apply(lambda x: [float(y) for y in x])
#another solution
df['col1'] = [[float(y) for y in x] for x in df['col1']]
print (df)
col1
0 [-0.8783137, 0.05478287, -0.08827557, 0.692039...
1 [0.31444644, -0.6546649, 0.7211526, 0.9819127,...
#dtype of lists is object
#https://stackoverflow.com/a/42672574/2901002
print (df['col1'].dtype)
object
#first value of column col1
print (df.loc[0, 'col1'])
[-0.8783137, 0.05478287, -0.08827557, 0.69203985, 0.06209986]
#type of first value of column col1 is list
print (type(df.loc[0, 'col1']))
<class 'list'>
#first value of column col1 and first value of list
print (df.loc[0, 'col1'][0])
-0.8783137
#first value of column col1 and type of first value of list
print (type(df.loc[0, 'col1'][0]))
<class 'float'>
EDIT2: If need DataFrame from lists - each list has same length:
df2 = pd.DataFrame(df['col1'].tolist(), index=df.index).astype(float)
print (df2)
0 1 2 3 4
0 -0.878314 0.054783 -0.088276 0.692040 0.062100
1 0.314446 -0.654665 0.721153 0.981913 0.740423