You can use this method but it will work only if both the list are of the same size:
first = [1, 2, 3, 4, 5]
second = [6, 7, 8, 9, 10]
third = []
a = len(first)
b = int(0)
while True:
x = first[b]
y = second[b]
ans = x + y
third.append(ans)
b = b + 1
if b == a:
break
print third