The five men were detained at the First District police station in Sofia while a further five were searched at a different precinct in the Bulgarian capital, taking the total number identified to 16, a spokeswoman for the ministry of the interior told PA.
Six supporters were arrested on Wednesday, with four already having been banned from attending any sporting event for the next two years and fined around £440. One individual faces a pre-trial hearing on Friday and could be remanded in custody.
The ministry spokeswoman said the search to identify further individuals continues.
England's black players were targeted for racial abuse throughout the match on Monday night.
The referee initiated the first step of UEFA's anti-racism protocol just before the half-hour mark by asking for a public address announcement in the stadium ordering the racist behaviour to stop.
The abuse continued and although there was a short stoppage just before half-time, the game was completed with England winning 6-0.
The Bulgarian Football Union, which is holding a press conference on Friday afternoon following the resignation of its president Borislav Mihaylov on Tuesday, has been charged by European football's governing body Uefa over the racist behaviour of its fans. The case will be heard on October 28.
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