how matching 2 locations on distance

General
1

...how i can match the nearest ingroup and outgroup upto 5 kms , i want to incorporate the distance between ingroup and outgroup please guide

2

Reprex

library(sf)
#> Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(leaflet)
library(charlatan)
# somewhere in pakistan...
ingroup <- data.frame(matrix(c(lat=33.74, lon=73.17), ncol = 2, byrow = F)) %>% 
  mutate(name = ch_name(1)) %>% 
  st_as_sf(coords = c("X1","X2"), crs=4326) 
ingroup
#> Simple feature collection with 1 feature and 1 field
#> geometry type:  POINT
#> dimension:      XY
#> bbox:           xmin: 33.74 ymin: 73.17 xmax: 33.74 ymax: 73.17
#> geographic CRS: WGS 84
#>               name            geometry
#> 1 Winston Shanahan POINT (33.74 73.17)

# somewhere else in pakistan...
outgroup <- data.frame(matrix(c(lat=33.60,lon=73.01), ncol = 2, byrow = F)) %>% 
  mutate(name = ch_name(1)) %>% 
  st_as_sf(coords = c("X1","X2"), crs=4326) 
outgroup
#> Simple feature collection with 1 feature and 1 field
#> geometry type:  POINT
#> dimension:      XY
#> bbox:           xmin: 33.6 ymin: 73.01 xmax: 33.6 ymax: 73.01
#> geographic CRS: WGS 84
#>             name           geometry
#> 1 Averie Zboncak POINT (33.6 73.01)

# find the nearest neighbour: sf::st_nearest_feature (computationally very efficient)
ingroup <- ingroup %>% 
  mutate(nearest_out = outgroup$name[st_nearest_feature(., outgroup)]) %>% 
  mutate(label = paste0("ingroup: <b>", name, "</b><br>nearest outgroup is: ", nearest_out))
#> although coordinates are longitude/latitude, st_nearest_points assumes that they are planar

# And now visualize the stuff!
leaflet() %>% 
  addTiles() %>% 
  addCircleMarkers(data=ingroup,lng=73.17,lat= 33.74, 
                   fillColor = "red", 
                   stroke = F, 
                   fillOpacity = .8,
                   popup = ~label) %>% 
  addCircleMarkers(data=outgroup,lng=73.01,lat= 33.60, 
                   fillColor = "blue",
                   stroke = F, 
                   fillOpacity = .8,
                   popup = ~name)%>% 
  addMarkers(lng=store$long,lat= store$lat,popup = "store ",group = "2")
#> Error in resolveFormula(lng, data): object 'store' not found