Can you recover deleted photos on iPhone 5s without any backup in place?

I deleted a bunch of holiday photos a couple months ago off my iPhone 5s (by mistake) and never thought to try and recover them until now.
I don't have iCloud or iTunes back up, are they still stored somewhere on my phone that I can access them?

If you maintained no back ups then deleted images are permanently lost.

The only exception is if the iPhone goes straight to a specialist data recovery company which will be able to try and recover raw data from the phone memory. Deleting a file does not automatically destroy it, it just makes the phone operating system forget where the data is and flags the memory locations as being available for re-use. So using the correct hardware and software, it's possible to recover such data even if the memory has been re-formatted. It only becomes irrecoverable if the memory locations get overwritten with new data such as if the iPhone has assigned new documents or images to memory previously holding your deleted pictures or if it's rearranged memory locations during a routine defragmentation or data compression.

But there are two major obstacles which will prevent it. First, specialist data recovery companies charge a huge amount for their services. Second, iPhones store data in an encrypted form, so even if you get the data back it will be completely unintelligible.

So in summary, your pictures are now a total loss and there's nothing you, or anyone else, can do about it.

You can't per se but there are ways. If you go to the apple store they might be able to recover it for a hefty price. My friend got her pictures back from one of the flagship stores. They told her it wasn't an ordinary procedure. Her phone still works like normal.