I am not suggesting anything is wrong, it is within normal limits for kids to have trouble with tying shoes and knowing how to tell the difference between left and right right shoes at this age.
If it continues after you spend time teaching him, or if he seems very resistant to practice or, if he seems to want to wear the shoes on the wrong feet even once you know that he knows the difference, then this could be a sign of sensory integration dysfunction. Again, it is NOT an issue an issue now, he is within normal limits for learning the skill at age 5, but I just like to get the information out there for you, and anyone else who might tune into your post who has an older child who is struggling with this.
Wearing the shoes on the wrong feet can give children with sensory processing issues more input in their feet, so they do this on purpose to boost their body awareness. Children who have difficulty learning to tie may be having issues with bilateral integration skills (doing activity where the hands have to work together and the right hand has to cross over the center of the body to do the task, and vice versa for the left) Writing is also affected in most kids too, so it is worth identifying early. It is common to see these two issues together.
If he only wears them backward about 50% of the time, you can assume that he is just putting the shoes on randomly, but if he always wears them backward, then pay very close attention because you might have the chance to help him early if it is something that needs greater intervention. Also look for resistance to using writing utensils, or leaning to one side or resting a the non writing hand on the side of the face while writing and then turning the whole body to change directions when he writes.
Many parents may not think to link problems like this with issues that they do notice early, like a speech or language issue, and miss a chance to do early intervention.
I am sure that your son will be fine and learn this with time and instruction.