Why do I get the "type mismatch" error when running the macro?

Not really an answer, more of a expanded comment.

If IsError(Cells(i, 5)) Then
    Cells(i, 5).Interior.Color = RGB(0, 0, 255)
ElseIf Cells(i, 5).Value = "" Then
    Cells(i, 5).Interior.Color = RGB(0, 0, 255)
Else
    Cells(i, 5).Interior.Color = xlNone
End If

Also, this to sift the errors https://docs.microsoft.com/en-us/office/vba/excel/concepts/cells-and-ranges/cell-error-values

First problem: If your cell contain an error, it doesn't contain the string "#N/A" or "#Ref", it contains a special value. What you see is only a visual representation of that error. If you want to check for an error within Excel, you should use the function IsError. That would lead to (wait, don't use that!):

If isError(Cells(i, 5).Value)
Or Cells(i, 5).Value = "Null" _
Or Cells(i, 5).Value = "" _
Or Cells(i, 5).Value Like "*-*" Then

Second problem: In VBA, there is no optimization for a conditional statement, VBA will always evaluate all parts. Your If-statement contains several conditions, combined with Or. While other programming languages quit evaluating when one condition makes the whole expression true, VBA will continue to evaluate all conditions.

Now if you have an error in a cell and you would use the code above, you will still get a type mismatch error: You cannot compare an error with a string. The condition isError(Cells(i, 5).Value) will get True, but VBA will continue to compare the cell content with strings and that gives you the mismatch. You need a way to split your If-statement.

Some more remarks: You are assigning the worksheet you want to work with to variable ws, but you are not using it. You will need to qualify every single usage of Cells (write ws.Cells(i, 5), else VBA will assume you are working with the Active Sheet, and that may or may not be Sheet1. Usually, this is done with a With-statement (note all the leading dots).

Your declaration statement is flawed (a common mistake in VBA), you will need to specify the type for every variable. In your case, Count will be of type Variant, not Long. No problem here, but in other cases it is, so make it a habit to declare all variables correctly.

You should use a For-Loop rather than a Do While.

Dim count As Long, i As Long
With ws
    count = .Cells(.Rows.count, "E").End(xlUp).Row
    For i = 2 to count
        Dim markCell as boolean
        If isError(.Cells(i, 5).Value) Then
            markCell = True       
        ElseIf .Cells(i, 5) = "Null" _
        Or .Cells(i, 5).Value = "" _
        Or .Cells(i, 5).Value Like "*-*" Then
            markCell = True
        Else
            markCell = False
        End If
        If markCell Then
            .Cells(i, 5).Interior.Color = RGB(38, 201, 218)
        End If
   Next i
End With

If you want to check for specific errors you first need to check if there are errors with IsError. You cannot check for an error and a value in one condition:

Do While i <= count
    Dim Condition As Boolean
    Condition = False  ' initialize when in a loop!
    
    If IsError(Cells(i, 5).Value) Then
        If Cells(i, 5).Value = CVErr(xlErrNA) _
             Or Cells(i, 5).Value = CVErr(xlErrRef) _
             Or Cells(i, 5).Value = CVErr(xlErrNull) _
             Or Cells(i, 5).Value = CVErr(xlErrDiv0) Then
                 Condition = True
        End If
    ElseIf Cells(i, 5).Value = "" Or Cells(i, 5).Value Like "*-*" Then
        Condition = True
    End If
    
    If Condition = True Then
        Cells(i, 5).Interior.Color = RGB(38, 201, 218)
    End If
Loop

Filter By Color

Sub FilterByColor()

    Const wsName As String = "Sheet1"
    Const Col As String = "E"
    Dim FilterColor As Long: FilterColor = RGB(38, 201, 218)

    Dim wb As Workbook: Set wb = ThisWorkbook ' workbook containing this code
    
    Dim ws As Worksheet: Set ws = wb.Worksheets(wsName)
    If ws.FilterMode Then ws.ShowAllData ' remove any filters
    
    Dim lRow As Long: lRow = ws.Cells(ws.Rows.count, Col).End(xlUp).Row
    
    Dim rgData As Range ' data range; no header
    Set rgData = ws.Range(ws.Cells(2, Col), ws.Cells(lRow, Col))
    rgData.Interior.Color = xlNone ' remove all colors
    
    Dim rgColor As Range ' the combined range to be colored
    Dim DataCell As Range ' each cell of the data range
    Dim cString As String
    Dim DoColor As Boolean
    
    For Each DataCell In rgData.Cells
        If IsError(DataCell) Then ' error value
            DoColor = True
        Else
            cString = CStr(DataCell.Value)
            If Len(cString) = 0 Then ' blank
                DoColor = True
            Else
                If InStr(1, cString, "-") > 0 Then ' contains a minus ('-')
                    DoColor = True
                End If
            End If
        End If
        If DoColor Then
            If rgColor Is Nothing Then ' combine cells into a range
                Set rgColor = DataCell
            Else
                Set rgColor = Union(rgColor, DataCell)
            End If
            DoColor = False ' don't forget to reset
        End If
    Next DataCell
        
    If rgColor Is Nothing Then Exit Sub
    
    rgColor.Interior.Color = FilterColor ' apply color in one go
    
    Dim rgTable As Range ' table range; header included
    Set rgTable = ws.Range(ws.Cells(1, Col), ws.Cells(lRow, Col))
    
    rgTable.AutoFilter 1, FilterColor, xlFilterCellColor
    
    ' To delete the rows, you could continue with e.g.:
'    rgData.SpecialCells(xlCellTypeVisible).EntireRow.Delete
'    ws.AutoFilterMode = False ' remove 'AutoFilter'
    
End Sub