Probably not. It takes 45 minutes to 1 hour on the NYAS express bus from terminal to Penn Station, about the same by LIRR and longer on the E subway. It takes about 15 minutes on the Airtrain to Jamaica Station and then about 20 minutes on LIRR, trains run frequently from Jamaica to Penn Station. I'd change your train to DC from 4:34 to the next available departure at 5:39.
Probably not. It takes 45