Sub-setting by group closest to defined value

I have a dataframe where I would like to select within each group the lines where y is the closest to a specific value (ex.: 5).

set.seed(1234)
df <- data.frame(x = c(rep("A", 4),
                       rep("B", 4)),
                 y = c(rep(4, 2), rep(1, 2), rep(6, 2), rep(3, 2)),
                 z = rnorm(8))

df

##   x y          z
## 1 A 4 -1.2070657
## 2 A 4  0.2774292
## 3 A 1  1.0844412
## 4 A 1 -2.3456977
## 5 B 6  0.4291247
## 6 B 6  0.5060559
## 7 B 3 -0.5747400
## 8 B 3 -0.5466319

The result would be:

##   x y          z
## 1 A 4 -1.2070657
## 2 A 4  0.2774292
## 3 B 6  0.4291247
## 4 B 6  0.5060559

Thank you, Philippe