The problem could be related to the adapter that is being used, we normally do not recommend to use adapter for the proper performance of the monitors, in this case you are using VGA which works with an analog signal to an HDMI that works with digital signal, and by doing that there could conflicts when you use this type of adapter.
Now, we can try the latest Intel® graphics driver for Intel® HD 5500 graphics controller, remember that the Intel® driver are generic, which means that they might or might not work with your system, and that is why we recommend to use the drivers provided by the manufacturer.
Here is the Beta driver 4539:
You can also try with driver 4501:
On the following link you will find the drivers provided by Dell, also you will see a file to do a BIOs update which will be a good thing to try as well:
If after trying the steps above the problem remains, then in that case it will be better to get in contact with Dell directly for further technical or warranty assistance.
Dell’s phone number: 1 800-624-9897
Dell’s support site: http://www.dell.com/support/home/us/en/04
Any questions, please let me know.
Thank you very much for letting us know that information.
In this case another option to try will be to get a monitor that has an HDMI port to avoid the usage of the converter, but of course we understand that option is not always available.
From our end the troubleshoot steps you tired are pretty much what we recommend to do in order to fix the problem, since the problem still persists the next thing to do will be to get in contact with the manufacturer of the laptop in this case Dell, for further technical or warranty assistance.
Any further questions, please let me know.