The short answer is Not likely.
The long answer is … [B]it depends[/B]. About 2-3 years ago, they upgraded the standard for HDMI to double the bandwidth for higher resolutions, implement HDCP, and a few other things I didn’t feel were important enough to recall, or search for.
HDMI V1 carried full H 1080p at 60fps + 8 channels of uncompressed audio. Your TV is Full HD 1080p, plus maybe 3 channel audio.
Newer cables have better screening, insulation & proper slightly higher thicker copper cables to comply with higher frequency signalling.
HDMI specification only covers limits for the path/cable, and so a short, poor quality cable will comply, whereas only a high quality cables will comply for long lengths.
Short cables (<5m) should be fine.
Your current HDMI cable should be fine.