Don;t know about specifics for condos, but I refinanced my long-time rental property (SFH) last year to a rate below 5%. To get the best rates you needed (at that time) 70% LTV (30% equity). I am unsure whether the current rates merit the costs of refinancing from 5.25. Get a quote from HLS and see.
Since it is only recently a rental and you have no rental history or tax returns reflecting the rental there may be other underwriting issues. But those rules tend to vary among lenders and loan programs and change over time. Best approach would be to refinance while living there (which I guess they did).
