islice has the advantage that it doesn't need to copy part of the list

from itertools import islice
for day in islice(days, 1, None):
    ...

First thing is to remember that python uses zero indexing.

You can iterate throught the list except using the range function to get the indexes of the items you want or slices to get the elements.

What I think is becoming confusing here is that in your example, the values and the indexes are the same so to clarify I'll use this list as example:

I = ['a', 'b', 'c', 'd', 'e']
nI = len(I) # 5

The range function will allow you to iterate through the indexes:

for i in range(1, nI):
    print(i)
# Prints:
# 1
# 2
# 3
# 4

If you want to access the values using the range function you should do it like this:

for index in range(1, nI):
    i = I[index]
    print(i)
# Prints:
# b
# c
# d
# e

You can also use array slicing to do that and you don't even need nI. Array slicing returns a new array with your slice.
The slice is done with the_list_reference[start:end:steps] where all three parameters are optional and:
start is the index of the first to be included in the slice
end is the index of the first element to be excluded from the slice
steps is how many steps for each next index starting from (as expected) the start (if steps is 2 and start with 1 it gets every odd index).
Example:

for i in I[1:]:
    print(i)
# Prints:
# b
# c
# d
# e

Using a for loop, how do I access the loop index, from 1 to 5 in this case?

Use enumerate to get the index with the element as you iterate:

for index, item in enumerate(items):
    print(index, item)

And note that Python's indexes start at zero, so you would get 0 to 4 with the above. If you want the count, 1 to 5, do this:

count = 0 # in case items is empty and you need it after the loop
for count, item in enumerate(items, start=1):
    print(count, item)

Unidiomatic control flow

What you are asking for is the Pythonic equivalent of the following, which is the algorithm most programmers of lower-level languages would use:

index = 0            # Python's indexing starts at zero
for item in items:   # Python's for loops are a "for each" loop 
    print(index, item)
    index += 1

Or in languages that do not have a for-each loop:

index = 0
while index < len(items):
    print(index, items[index])
    index += 1

or sometimes more commonly (but unidiomatically) found in Python:

for index in range(len(items)):
    print(index, items[index])

Use the Enumerate Function

Python's enumerate function reduces the visual clutter by hiding the accounting for the indexes, and encapsulating the iterable into another iterable (an enumerate object) that yields a two-item tuple of the index and the item that the original iterable would provide. That looks like this:

for index, item in enumerate(items, start=0):   # default is zero
    print(index, item)

This code sample is fairly well the canonical example of the difference between code that is idiomatic of Python and code that is not. Idiomatic code is sophisticated (but not complicated) Python, written in the way that it was intended to be used. Idiomatic code is expected by the designers of the language, which means that usually this code is not just more readable, but also more efficient.

Getting a count

Even if you don't need indexes as you go, but you need a count of the iterations (sometimes desirable) you can start with 1 and the final number will be your count.

count = 0 # in case items is empty
for count, item in enumerate(items, start=1):   # default is zero
    print(item)

print('there were {0} items printed'.format(count))

The count seems to be more what you intend to ask for (as opposed to index) when you said you wanted from 1 to 5.

Breaking it down - a step by step explanation

To break these examples down, say we have a list of items that we want to iterate over with an index:

items = ['a', 'b', 'c', 'd', 'e']

Now we pass this iterable to enumerate, creating an enumerate object:

enumerate_object = enumerate(items) # the enumerate object

We can pull the first item out of this iterable that we would get in a loop with the next function:

iteration = next(enumerate_object) # first iteration from enumerate
print(iteration)

And we see we get a tuple of 0, the first index, and 'a', the first item:

(0, 'a')

we can use what is referred to as "sequence unpacking" to extract the elements from this two-tuple:

index, item = iteration
#   0,  'a' = (0, 'a') # essentially this.

and when we inspect index, we find it refers to the first index, 0, and item refers to the first item, 'a'.

>>> print(index)
0
>>> print(item)
a

Conclusion

• Python indexes start at zero
• To get these indexes from an iterable as you iterate over it, use the enumerate function
• Using enumerate in the idiomatic way (along with tuple unpacking) creates code that is more readable and maintainable:

So do this:

for index, item in enumerate(items, start=0):   # Python indexes start at zero
    print(index, item)