Use one primer from the backbone (ex T7 promoter region) and one primer from your gene-of-interest (GOI) to verify your cloning result, and GOI's orientation in the plasmid. You should obtain a single PCR band.

You can also find out by adding an empty DH5a cells (no vectors) in your next PCR as a control to see whether anything get amplified.

DH 5 alpha  is very strange in its characteristic. It sometimes carry both T7  and SP6. It has been observed that most frequently it carries SP6 as compared to T7 and sometime it does not carry both the genes. t  agree with Yuan-Yeu, that  you add empty DH 5 alpha as a control in PCR. 

It is not clear to me what is your problem, you could see double band after some ENase digestion analysis of recombinant plasmids, I mean 300 bp and something extra above it? Some restriction endonuclease preparation ("old" with mostly denatured enzymes) gives an effect of DNA retardation (migration of DNA -enzyme complex) after resolution on agarose gel. Maybe this is your case. Try another restriction enzyme which can cut out your insert. T7 and SP6 promoters come only from pGEM not from DH5a host.