AKMV 
The possibilities for granting citizenship are governed by Act No. 40/1993 Coll. on the citizenship of the Slovak Republic.
An applicant who has married a citizen of the Slovak Republic and has a permitted stay on the territory of the Slovak Republic may apply for citizenship no earlier than after five (5) years immediately preceding the application. The condition is that at the time of the application the marriage still exists and the spouses live together in a common household on the territory of the Slovak Republic.
If the applicant is not the spouse of a Slovak citizen, the law requires uninterrupted permanent residence of at least eight (8) years immediately preceding the application, or uninterrupted residence of at least ten (10) years if the applicant already had permanent residence at the time of the application.
From your question, it does not appear that any exceptions according to § 7 paragraphs 2 to 6 of the Citizenship Act apply, where an application may be submitted even after a shorter stay than five years in the territory of the Slovak Republic (e.g., if the applicant has been issued a certificate proving the status of a Slovak living abroad, an applicant who has significantly contributed to the Slovak Republic, etc.).