This seems an improvement:
> cols<-!(colnames(dt) %in% c("V1","V2","V3","V5"))
> new_dt<-subset(dt,,cols)
> cor(new_dt)
V4 V6 V7 V8 V9 V10
V4 1.0000000 0.14141578 -0.44466832 0.23697216 -0.1020074 0.48171747
V6 0.1414158 1.00000000 -0.21356218 -0.08510977 -0.1884202 -0.22242274
V7 -0.4446683 -0.21356218 1.00000000 -0.02050846 0.3209454 -0.15021528
V8 0.2369722 -0.08510977 -0.02050846 1.00000000 0.4627034 -0.07020571
V9 -0.1020074 -0.18842023 0.32094540 0.46270335 1.0000000 -0.19224973
V10 0.4817175 -0.22242274 -0.15021528 -0.07020571 -0.1922497 1.00000000
This one is not quite as easy to grasp but might have use for situations there there were a need to specify columns by a numeric vector:
subset(dt, , !grepl(paste0("V", c(1:3,5),collapse="|"),colnames(dt) ))