Heater Not Heating, Then Getting Too Hot

I have the Aqueon Pro 50 watt heater in my 5 gallon tank. I don't have any fish in it yet but there will be soon. I'm trying to get the temperature ready and steady for them but the heater is driving me crazy.
This morning I set it to 79-80 degrees F (the water was room temp) and when I got home 7 hours later the temperature had barely moved. I put the dial up a notch or two and then it started to get too hot (but I wondered if it was actually trying to go to that temperature this time). So, I turned it down. But the red light still comes on like it's heating. The green light rarely comes on at all. It keeps getting hotter and I'm worried.
Also, this may be worth noting- at first when it showed the green light every few seconds or so there'd be a flash of red which was weird.
Now I have it set on about 78 and so far the temp reads 81. The red light is on and I felt the heater to make sure- it's warm.

EDIT: The green light just came on. The dial is still set to 78 and the thermometer still reads 81. Maybe it'll cool down a little? Either way, 81 isn't bad at all.

 

What thermometer is it?

 

Not an expert with heaters, but you can unplug it and see where it goes.

So, your talking about the Aqueon brand, I thought you said the Marineland brand on your other thread.

Just what Aster said, I've heard stick on the wall thermometers are unaccurate , but I seem to have success with them.

 

I'm really doubting the accuracy of that thermometer especially if since you said it was reading 100° on the first day on the other thread.

You can test the accuracy by getting a cup and filling it with completely with ice cubes, then fill it it up to just below the ice with chilled water. This website explains it further.
Testing Thermometers For Accuracy: Ice Bath Test & Boiling Water Test - The Virtual Weber Bullet

Not an expert with heaters, but you can unplug it and see where it goes.

So, your talking about the Aqueon brand, I thought you said the Marineland brand on your other thread.

Just what Aster said, I've heard stick on the wall thermometers are unaccurate , but I seem to have success with them.

Her tank is Marineland, but the heater is Aqueon

 

You can also use a kitchen thermometer.