The statute of limitations on a crime are different depending on the crime alleged. If the crime is a gross misdemeanor, the prosecution must begin before two years. For this to be the case, the television would have to be worth less than $250 and have no other crimes alleged (such as burglary or robbery) which could make the crimes felonies. If the television is worth more than $250 the statute of limitations would be 3 years (without any other crimes alleged). This is not always a straight calculation of years. If the person charged is "not usually and publicly resident within this state" that time does not apply, and it can be tolled for other reasons as well.
First one has to determine the value of the stolen TV five years ago; if, at that time, it was worth less than $250, the charge would be theft third degree, a gross misdemeanor, and charges would need to have been filed within two years. If the TV was worth more than $250 five years ago, the charge is either a theft second degree, or if valued at over $1500, theft first degree. Theft first and second degree are both felonies, with statutes of limitations expiring in three years.
However, your question asks whether the person can be arrested more than five years after the crime; the answer to this question is "yes", if in fact a theft charge was filed within the three year statute of limitations and he/she failed to appear for court or was otherwise unavailable or outside of the jurisdicition. Once a charge is filed and a defendant does not appear in court, a warrant of arrest is issued. This tolls(stops) the 3 year statute of limitations from expiring. This means that the case remains open so long as that person is still at large on warrant status.
The three year statute of limitations only requires that charges be FILED within three years of the crime's commission; the notion that a person can just "lay low" for three years and that case will automatically be dismissed is incorrect as long as a warrant on the charge remains outstanding.
In addition to the answers previously given regarding statutes of limitation it is important to remember that if a case has been filed for that particular offense no passage of time will prevent an arrest. A warrant for arrest can stay in the system indefinitely. After arrest and charge the person may have a defense that the authorities sat on their right to arrest the person and therefore prejudiced the person's due process rights to a speedy trial. But since your question was can he/she be arrested? The answer is "Yes".
In general, five years would be beyond the statute of limitations in every state. However, it does depend on how the crime is charged. Also, there are instances that toll the statute of limitations for a crime. If the person is out of the state or country the clock will typically stop for statute of limitation purposes.