typescript-eslint-parser is now pulling in eslint@4.19.1, ideally it should be asking for a peer dependency of "eslint": ">=4.19.1". This would allow de-duplication of the eslint dependency in consumers of typescript-eslint-parser using a different version of eslint.

A current workaround is to pin the eslint dependency in a consuming project using a resolution. For example, to force using eslint@^5.0.0

"resolutions": {
  "eslint": "^5.0.0",
}