Is it acceptable for a first class letter I posted to take 5 days to travel 30 miles,?

if you think that timing is bad, the my story of a 1st class letter posted one for delivery the next day at an address 2miles away, the letter never arrived.. the royal mail 1st class mail is little more than a con job..

No.

No it isn't. Why does it take her five days to walk that short distance?

You could have walked there with the letter and saved the 70p.

George Osborne privatised royal mail. The private company wants you to pay around £7 to guarantee that they won't lose your letter and deliver it, you must pay that to ensure it doesn't take a long time. The recorded "signed for" services are still not guaranteed, you have to pay £6-7 to actually ensure a letter gets there. Absolutely vile.

No, but somebody may not like her head on the stamp.

Go knock on her door and tell her in person.