Based on the lmtest package manual, you appear to have five continuous predictors (and maybe some categorical predictors) in your model. We know there are five continuous predictors because your first degrees of freedom is 5, and you can only add squared continuous variables to a model, not squared dummy variables as stated in the manual.
These predictors were squared (
power = 2) and added to the original model to create a new model. And an F-test was used to compare your original model to this new model. The F-test was statistically significant suggesting that at least one of the squared continuous predictors is a statistically significant predictor of your outcome.
Your second degrees of freedom is large, so you have a huge sample size, large enough to detect even trivial effects. Even if the relationship is slightly quadratic, you have the power to detect it. Without an explanation of the context, access to the coefficients, some diagnostic plots, one cannot know how problematic your misspecification is.
Note that the RESET test is a test for functional form specification not omitted variable bias (OVB). And OVB might affect some variables while others are not affected. The simplest answer to your question about OVB is yes, it is present. Since you have multiple predictors and individuals were most likely not randomized to have those values of the predictors, there will be OVB.
The package manual and Wikipedia do a decent job of explaining the test. Section 6.2.3 of Wooldridge's Econometric analysis of cross section and panel data (2010) clarifies what the RESET test is and misconceptions about it like its (in)ability to test for OVB.