John 20:5 describes John's reaction upon reaching the tomb of Jesus after Mary Magdalene reported it being empty. "Stooping and looking in, he saw the linen cloths lying, yet he didn’t enter in." Let's break down the meaning:

"Stooping and looking in": This indicates that the tomb entrance was likely low, requiring John to bend down to see inside.
"He saw the linen cloths lying": The linen cloths were the burial cloths that had been wrapped around Jesus' body. Their presence suggested a careful, deliberate removal, rather than a frantic theft. They weren't discarded haphazardly but were "lying" there.
"Yet he didn’t enter in": This is the key part. John stopped at the entrance and didn't go inside.

Here's what we can infer from this verse:

Respect and hesitation: John's hesitation to enter may suggest a mix of reverence and uncertainty. This was a deeply unsettling and potentially supernatural event.
Peter's impetuosity: The next verse (John 20:6) tells us that Peter arrived soon after and immediately went into the tomb. John's reluctance contrasts with Peter's more impulsive nature. This comparison highlights the different personalities of the two disciples.
Evidence of resurrection, not theft: The fact that the linen cloths were still there, neatly arranged, was crucial evidence that the body had not been stolen. Grave robbers would typically take the body and leave the cloths behind or take everything. The state of the linen cloths hinted at something more extraordinary.
Setting the stage for Peter: John's not entering creates anticipation. It allows Peter's entrance and subsequent discovery to be the focal point. It also heightens the impact of what Peter sees inside.

In essence, John's actions in this verse contribute to the mystery and suspense surrounding the empty tomb, while also subtly highlighting the different responses and personalities of the disciples in the face of the inexplicable. He observes, notes the evidence, but pauses, perhaps overwhelmed or unsure of what to do next.