I would use the following modification of your example sentence: 'There will be a five-percent raise across the board. Additionally, all staff will receive an extra five days leave per year'.
The context of your sentence appears to be an announcement by the management of a company to its employees. These type of communications tend to be more formal grammatically than used in spoken English, which is often much more casual in grammar. Replacing 'Additionally' with ether 'besides' or 'besides that' is much more informal. Someone might use 'besides' rather than 'additionally' when speaking casually but a company making a formal announcement would not normally write the sentence that way, especially if the announcement is a written communication.